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Double cover Lie group of the special orthogonal group
mathematics the spin group, denoted Spin(n), is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n,
Spin_group
Non-tensorial representation of the spin group
or "spin", of the electron and other subatomic particles. Mathematically, spinors are elements of spaces carrying representations of the spin group or
Spinor
Concept in differential geometry
and the spin representation of its structure group Spin(n) on the space of spinors Δn. The bundle S is called the spinor bundle for a given spin structure
Spin_structure
Algebra based on a vector space with a quadratic form
representations of the pin group Pinp,q(R). On restriction to the spin group Spinp,q(R) these become isomorphic, so the spin group has a complex spinor representation
Clifford_algebra
Topics referred to by the same term
Look up spin or spinning in Wiktionary, the free dictionary. Spin or spinning most often refers to: Spin (physics) or particle spin, a fundamental property
Spin
Type of group in mathematics
special orthogonal group, the corresponding groups are: Spin group, Spin(n) → SO(n), Projective special orthogonal group, SO(n) → PSO(n). Spin is a 2-to-1 cover
Orthogonal_group
Twisted spin group
In spin geometry, a spinc group (or complex spin group) is a Lie group obtained by the spin group through twisting with the first unitary group. C stands
Spinc_group
Intrinsic quantum property of particles
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms
Spin_(physics)
Matrix representing a Euclidean rotation
universal covering group. Often the covering group, which in this case is called the spin group denoted by Spin(n), is simpler and more natural to work with
Rotation_matrix
Particular projective representations of the orthogonal or special orthogonal groups
In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension
Spin_representation
Mathematical description of fermions
the action of the Lorentz group, which describes the symmetries of Minkowski spacetime. They occur in the relativistic spin-1/2 wave function solutions
Dirac_spinor
Twisted spin group
spin geometry, a spinh group (or quaternionic spin group) is a Lie group obtained by the spin group through twisting with the first symplectic group.
Spinh_group
Nonabelian group of order 120
\operatorname {Spin} (3)\to \operatorname {SO} (3)\,} of the special orthogonal group by the spin group. It follows that the binary icosahedral group is a discrete
Binary_icosahedral_group
Geometric structure
{\displaystyle \rho \colon {\mathrm {Spin} }(n)\to {\mathrm {SO} }(n)} of the special orthogonal group by the spin group. The spinor bundle S {\displaystyle {\mathbf
Spinor_bundle
Form of propaganda in public relations and politics
In public relations and politics, spin is a form of propaganda, achieved through knowingly providing a biased interpretation of an event. While traditional
Spin_(propaganda)
\operatorname {Spin} (3)\to \operatorname {SO} (3)} of the special orthogonal group by the spin group. It follows that the binary octahedral group is a discrete
Binary_octahedral_group
Phenomenological model in criminology
the criminal theory. The criminal spin indicates acute and chronic spin, as well as individual, group and community spin. A basic premise of this theory
Criminal_spin
Topics referred to by the same term
represent spins and rotations of quantum states and tensor operators. Higher spin alternating sign matrix Spin group Spin (physics)#Higher spins This disambiguation
Spin_matrix
American rock band
The Spin Doctors are an American alternative rock band from New York City, best known for their early 1990s hits "Two Princes" and "Little Miss Can't Be
Spin_Doctors
Canadian toy and entertainment company
Spin Master Corp. (formerly known as Spin Master Toys) is a Canadian multinational toy and entertainment company headquartered in Toronto, Ontario. Spin
Spin_Master
Algebraic structure
homomorphism Spin ( 3 ) → SO ( 3 ) {\displaystyle \operatorname {Spin} (3)\to \operatorname {SO} (3)\,} of the special orthogonal group by the spin group. As
Binary_cyclic_group
Concept in topological group theory
covering group, a topological double cover in which the kernel of p has order two; examples include the spin groups, pin groups, and metaplectic groups. Roughly
Covering_group
Representation of the symmetry group of spacetime in special relativity
finite-dimensional representation theory of the universal covering group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Classification in abstract algebra
algebra, not to the spin group. Let (V,q) be a real quadratic space. The spin group is defined inside the even Clifford algebra by Spin ( V , q ) = Pin
Classification of Clifford algebras
Classification_of_Clifford_algebras
Subgroup of the Clifford algebra associated to a quadratic space
group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps
Pin_group
Action where a company splits off part as a separate entity
A corporate spin-off, also known as a spin-out, starburst or hive-off, is a type of corporate action where a company "splits off" a section as a separate
Corporate_spin-off
Quantum state of a system
happened is that the two conjugate 2-dimensional spin representations of the spin group SU(2) = Spin(3) (as it sits inside the 3-dimensional Clifford
Triplet_state
Nonabelian group in algebraic group theory
group by the spin group. It follows that the binary tetrahedral group is a discrete subgroup of Spin(3) of order 24. The complex reflection group named 3(24)3
Binary_tetrahedral_group
Geometric symmetry operation
n ) {\displaystyle -1\in \mathrm {Spin} (n)} in the spin group. This is particularly confusing for even spin groups, as − I ∈ S O ( 2 n ) {\displaystyle
Point_reflection
1998 studio album by Danny Wilde + The Rembrandts
Spin This is a solo album by The Rembrandts' Danny Wilde, released by Elektra Records in 1998. The album is credited to "Danny Wilde + The Rembrandts."
Spin_This
Diagram used to represent quantum field theory calculations
representations of matrix groups. The diagrammatic notation can thus greatly simplify calculations. Roger Penrose described spin networks in 1971. Spin networks have
Spin_network
Topological group with compact topology
the circle group T and the torus groups Tn, the orthogonal group O(n), the special orthogonal group SO(n) and its covering spin group Spin(n), the compact
Compact_group
Relativistic wave equation describing massless fermions
the spin group as the fiber. The spin group S p i n ( p , q ) {\displaystyle \mathrm {Spin} (p,q)} is a double cover of the special orthogonal group S
Weyl_equation
1997 single by Sneaker Pimps
"Spin Spin Sugar" is a song by English electronic band Sneaker Pimps, released in March 1997 by Clean Up as the fourth single from their debut studio
Spin_Spin_Sugar
Matrices important in quantum mechanics and the study of spin
projective representation (spin representation) of the rotation group SO(3) acting on non-relativistic particles with spin 1⁄2. The states of the particles
Pauli_matrices
Grand Unified Theory proposed in 1973
the spin group Spin(10). The shortened name SO(10) is conventional among physicists, and derives from the Lie algebra or less precisely the Lie group of
SO(10)
American television series (1996–2002)
Spin City is an American sitcom television series that aired from September 17, 1996, to April 30, 2002, on ABC. Created by Gary David Goldberg and Bill
Spin_City
Low-rank isomorphisms in mathematics
between rotation groups and spinors. More precisely, these are low-rank isomorphisms or central isogenies among classical algebraic groups that arise from
Exceptional isomorphisms of classical groups
Exceptional_isomorphisms_of_classical_groups
Group of flat spacetime symmetries
Lorentz-signature spin group Spin ( 1 , 3 ) {\displaystyle \operatorname {Spin} (1,3)} . The Poincaré algebra is the Lie algebra of the Poincaré group. It is a
Poincaré_group
Group of unitary complex matrices with determinant of 1
symmetry groups of spinors, Spin(3), that enables a spinor presentation of rotations. The special unitary group SU(n) is a strictly real Lie group (vs. a
Special_unitary_group
Group that is also a differentiable manifold with group operations that are smooth
integer spin and half-integer spin in quantum mechanics. Other examples of simply connected Lie groups include the special unitary group SU(n), the spin group
Lie_group
1989 studio album by Yellowjackets
Performance, Group" category. It peaked in the top 10 on Billboard's Jazz Albums chart. Yellowjackets had originally hoped to record The Spin with Claus
The_Spin
Molecular orbital theory applied to transition metal complexes
low-spin, while the latter is called high-spin. A small ΔO can be overcome by the energetic gain from not pairing the electrons, leading to high-spin. When
Ligand_field_theory
Real square matrix whose columns and rows are orthogonal unit vectors
with a covering group of SO(n), the spin group, Spin(n). Likewise, O(n) has covering groups, the pin groups, Pin(n). For n > 2, Spin(n) is simply connected
Orthogonal_matrix
Groups of point isometries in 3 dimensions
Spin(3) → SO(3) is the double cover of the rotation group by the spin group in 3 dimensions. (This is the only connected cover of SO(3), since Spin(3)
Point groups in three dimensions
Point_groups_in_three_dimensions
Relativistic wave description of fermions
\operatorname {Spin} (1,3).} This stands in contrast to the Dirac spinors, which are only covariant under the action of the complexified spin group Spin C (
Majorana_equation
Spinning motion in theoretical physics
theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in
Spin_tensor
Relativistic interaction in quantum physics
mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion
Spin–orbit_interaction
Rotation group in 8-dimensional Euclidean space
SO(8) is the spin group Spin(8). The center of SO(8) is Z2, the diagonal matrices {±I} (as for all SO(2n) with 2n ≥ 4), while the center of Spin(8) is Z2×Z2
SO(8)
Object in geometric algebra
vector space V is the same thing as an element of the spin group Spin(V). We define this group below. Let V be a vector space equipped with a positive
Rotor_(mathematics)
Infinite-dimensional group in topology
{\displaystyle 3} -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in
String_group
Relationship between certain vector spaces
D4 and the associated Lie group Spin(8), the double cover of 8-dimensional rotation group SO(8), arising because the group has an outer automorphism of
Triality
Symmetry of physical laws under a charge-conjugation transformation
transform according to the spin group. Building a principle fiber bundle with the spin group as the fiber results in a spin structure. All that is missing
C-symmetry
Lie group of Lorentz transformations
fundamental group has order 2, and its universal cover, the indefinite spin group Spin(1, 3), is isomorphic to both the special linear group SL(2, C) and
Lorentz_group
American media company, spin-off from Comcast
multinational mass media and technology company. Formed on January 2, 2026, as a spin-off of Comcast, Versant is headquartered at 229 West 43rd Street in Midtown
Versant
Group in mathematical representation theory
symplectic group itself, but a double cover of it. That double cover is the metaplectic group. This phenomenon is closely analogous to the role of the spin group
Metaplectic_group
American music magazine
Spin (stylized in all caps as SPIN) is an American music magazine founded in 1985 by publisher Bob Guccione Jr. Later owned by Next Management Partners
Spin_(magazine)
Connection on a spinor bundle
In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the
Spin_connection
Topics referred to by the same term
Look up spin-off or spin off in Wiktionary, the free dictionary. Spin-off, Spin Off, Spin-Off, or Spinoff may refer to: Spinoff (media), a media work
Spin-off
positive definite groups. Like the spin groups and pin groups, which are covers rather than quotients of the (special) orthogonal groups, the projective
Projective_orthogonal_group
Clifford algebra in 4 dimensions
exponentiate to a representation of the spin group Spin ( 1 , 3 ) {\displaystyle {\text{Spin}}(1,3)} of the Lorentz group SO ( 1 , 3 ) {\displaystyle {\text{SO}}(1
Dirac_algebra
1969 studio album by Four Tops
Soul Spin is the eighth studio album by American soul music vocal group Four Tops, released by Motown. A review in Billboard recommends this album to retailers
Soul_Spin
Special tangential structure
In spin geometry, a spinc structure (or complex spin structure) is a generalization of a spin structure. In mathematics, these are used to describe spinor
Spinc_structure
Subspace defined by a polynomial of degree 2 over a field
is the spin group Spin(n), and there is a standard way to extend the spin representations of Spin(n) to representations of P. (There are two spin representations
Quadric_(algebraic_geometry)
International figure skating competition
The Golden Spin of Zagreb (Croatian: Zlatna pirueta Zagreba) is an annual figure skating competition sanctioned by the International Skating Union (ISU)
Golden_Spin_of_Zagreb
2022 political science book
China. The authors contend that modern "spin dictators" pretend to be democrats (for example, allowing a select group of high-brow, but low-circulation, dissident
Spin_Dictators
Concept in mathematics
+x_{2n-1}x_{2n}+x_{2n+1}^{2};} Cn: the symplectic group Sp(2n) over k; Dn: the spin group Spin(2n) associated to a quadratic form of dimension 2n over
Reductive_group
Type of group in mathematics
corresponding simply connected cover is the spin group. In the split case this recovers the ordinary groups P G O + ( V , q ) {\displaystyle \mathrm {PGO}
Classical_group
Aviation term for a corkscrew downward path
In flight dynamics, a spin is a special category of stall resulting in autorotation (uncommanded roll) about the aircraft's longitudinal axis and a shallow
Spin_(aerodynamics)
these as discrete subgroups (point groups). The special orthogonal group has a 2-fold cover by the spin group Spin(n) → SO(n), and restricting this cover
Covering groups of the alternating and symmetric groups
Covering_groups_of_the_alternating_and_symmetric_groups
Special tangential structure
In spin geometry, a spinh structure (or quaternionic spin structure) is a generalization of a spin structure. In mathematics, these are used to describe
Spinh_structure
Technique for isolating and observing short-lived free radical molecules
short-lived radicals was developed by several independent groups by 1968. The most commonly used spin traps are alpha-phenyl N-tertiary-butyl nitrone (PBN)
Spin_trapping
Japanese rock band
Gacharic Spin is a Japanese rock band formed in Tokyo in 2009. Initially releasing music independently, they later signed with Victor Entertainment then
Gacharic_Spin
State space for internal degrees of freedom of a subatomic particle
number of the map. SU ( 2 ) ≅ Spin ( 3 ) {\displaystyle {\text{SU}}(2)\cong {\text{Spin}}(3)} : Part of the gauge group of the Standard model. Irreps
Multiplet
Class of spinors constructed using Clifford algebras
pure spinor. In terms of stratification of spinor modules by orbits of the spin group S p i n ( V , Q ) {\displaystyle Spin(V,Q)} , pure spinors correspond
Pure_spinor
Generators of the Clifford algebra for relativistic quantum mechanics
group is encoded in the spin group Spin(1, 3) (for real, uncharged spinors) and in the complexified spin group Spin(1, 3) for charged (Dirac) spinors
Gamma_matrices
This is an episode list for the American sitcom television series Spin City. The series, which premiered on ABC on September 17, 1996, stars Michael J
List_of_Spin_City_episodes
The discography of the Spin Doctors, an American rock band, consists of seven studio albums, three live albums, four compilation albums, and fourteensingles
Spin_Doctors_discography
Pakistani politician and businessman
his group's business operations in the textile industry. Ejaz Textile Mills Limited was established in Bhai Pheru in 1990, followed by Ejaz Spinning Mills
Sheikh_Ejaz_Ahmad
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
This group is not simply connected however: its universal (double) cover is the spin group. Cr has as its associated simply connected group the group of
Simple_Lie_group
American fashion holding company
would spin off its "cable holdings and other non-retail assets" into the new company Liberty Ventures, with Liberty Interactive to be renamed QVC Group. QVC
QVC_Group
Anticommutating number
anti-commuting Weyl spinors. Both the anti-commutation and the expression as spinors arises in a natural fashion for the spin group. In essence, the Grassmann
Grassmann_number
Spinor topology
relating to the geometry of spinors or alternatively as a concrete realization of the failure of the special orthogonal groups to be simply connected. Spatial
Orientation_entanglement
2006, the company acquired the Spin Palace Group for approximately US$65 million. Casinos owned by the group included: Spin Palace Casino Ruby Fortune Casino
Fairground_Gaming
Mathematical group
Spin 0 ( 1 , 2 ) {\displaystyle \operatorname {Sp} (2,\mathbb {R} )\cong \operatorname {Spin} _{0}(1,2)} . This is because the special linear group
Symplectic_group
Digital gaming and sports betting company
multi-brand online casino Spin. Super Group was founded with a focus on online gaming and sports betting. In January 2022, Super Group listed on the New York
Super_Group_(company)
Method of turning fiber into yarn or thread
Spinning is a twisting technique to form yarn from fibers. The fiber intended is drawn out, twisted, and wound onto a bobbin. A few popular fibers that
Spinning_(textiles)
Mathematical coincidence
integers; S1 ≅ Spin(2) ≅ SO(2) ≅ U(1) ≅ R / Z ≅ circle group; S3 ≅ Spin(3) ≅ SU(2) ≅ Sp(1) ≅ unit quaternions. In addition to Spin(1), Spin(2) and Spin(3) above
Exceptional_isomorphism
Quantum process reducing the variance of spin along a particular axis
particles with spin. This is achieved by somehow entangling the individual spin states within the ensemble.The quantum states obtained are called spin squeezed
Spin_squeezing
Spin representations of the SO(3) group
part of the detailed algebraic discussion of the rotation group SO(3). The association of a spinor with a 2×2 complex traceless Hermitian matrix was formulated
Spinors_in_three_dimensions
2005 science fiction novel by author Robert Charles Wilson
Spin is a science fiction novel by American-Canadian writer Robert Charles Wilson. It was published in 2005 and won the Hugo Award for Best Novel in 2006
Spin_(novel)
1990 single by Hi Tek 3 featuring Ya Kid K
"Spin That Wheel" is a song by Hi Tek 3 in collaboration with Belgian group Technotronic members Ya Kid K and Jo Bogaert. It was released under the name
Spin_That_Wheel
Topological space with only one nontrivial homotopy group
complex spin group is a group extension 0 → K ( Z , 1 ) → Spin C ( n ) → Spin ( n ) → 0 {\displaystyle 0\to K(\mathbb {Z} ,1)\to \operatorname {Spin} ^{\mathbb
Eilenberg–MacLane_space
Tool for verifying the correctness of software models
SPIN is a general tool for verifying the correctness of concurrent software models in a rigorous and mostly automated fashion. It was written by Gerard
SPIN_model_checker
Chief executive officer of BBC Worldwide from 2004 until 2012
Architects (in the same year as John Prescott). He is currently Chairman of Spin Group Ltd, Jungle Creations Ltd, Seeker Music Publishing. "John Barry SMITH
John_Smith_(BBC_executive)
2018 American film
Spinning Man is a 2018 thriller film directed by Simon Kaijser based on a novel by George Harrar and adapted to screenplay by Matthew Aldrich. It stars
Spinning_Man
Type of cyclic group in group theory
dicyclic group is a binary polyhedral group — it is one of the classes of subgroups of the Pin group Pin−(2), which is a subgroup of the Spin group Spin(3)
Dicyclic_group
Retrieved August 5, 2012. The 10 Best TV Spin-offs of All Time The 10 best (and worst) spinoff shows of all time, ranked Top 10 Worst TV Spin-Offs - TIME
List_of_television_spinoffs
A spin valve is a device, consisting of two or more conducting magnetic materials, whose electrical resistance can change between two values depending
Spin_valve
American actress (born 2005)
cinema and had her first lead role in the Disney Channel original movie Spin (2021) and subsequently starred in Netflix's Senior Year (2022). She gained
Avantika_(actress)
SPIN GROUP
SPIN GROUP
Girl/Female
Australian, Biblical, Kurdish
Bush
Male
French
Old French name, possibly derived from the word pepin/pipin, PÉPIN means "seed of a fruit."
Girl/Female
Native American
Spins.
Male
Babylonian
, I trust in Sin!
Girl/Female
Biblical
Rare, precious.
Girl/Female
Indian
Glowing skin
Boy/Male
Australian, Spanish
Innocent
Boy/Male
Egyptian
Light skin.
Surname or Lastname
English
English : from Middle English spink ‘chaffinch’ (probably of imitative origin), hence a nickname bestowed on account of some fancied resemblance to the bird.
Boy/Male
British, Danish, English, Norwegian
Skin; Parchment
Surname or Lastname
English and Irish
English and Irish : (of Norman origin): habitational name from Épaignes in Eure, recorded in the Latin form Hispania in the 12th century. It seems to have been so called because it was established by colonists from Spain during the Roman Empire.English and Irish : habitational name from Espinay in Ille-et-Vilaine, Brittany, so called from a collective of Old French espine ‘thorn bush’.English and Irish : ethnic name for a Spaniard or, in the case of the Irish name, for someone returning from Spain (from Gaelic Spainneach ‘Spanish’); many Irish took refuge in Spain during the 17th century wars.
Male
Japanese
(1-晋, 2-信, 3-紳, 4-心, 5-慎, 6-新, 7-進, 8-真) Japanese name SHIN means 1) "advancing," 2) "belief," 3) "gentleman," 4) "heart," 5) "humble," 6) "new," 7) "progressive," and 8) "true." Compare with another form of Shin.
Boy/Male
Indian, Sanskrit
Skin of a Goat; Tiger Skin
Biblical
rare; precious
Girl/Female
Muslim
Glowing skin
Girl/Female
Australian, Indian, Punjabi, Sikh
Quite and Gentle
Female/Male/Unisex
Korean
Korean name SHIN means "faith, trust." Compare with another form of Shin.
Boy/Male
Indian
Life Span
Biblical
a bush, enmity
Girl/Female
Christian, Hindu, Indian
Dark Skin
SPIN GROUP
SPIN GROUP
Boy/Male
Tamil
Peacock
Boy/Male
British, English
From the Deer Park
Girl/Female
Arabic, Bengali, Danish, Farsi, French, Hindu, Indian, Indonesian, Iranian, Italian, Jain, Japanese, Kannada, Lebanese, Malayalam, Marathi, Muslim, Oriya, Tamil, Telugu
White Antelope; Siddhi will Follow; Rhyme; Poetry; Gem
Boy/Male
Celtic Gaelic Welsh Irish
Gentle.
Male
Hebrew
(לִי-×¢Ö¸×) Hebrew name LIAM means "my nation, my people." Compare with another form of Liam.
Girl/Female
Tamil
Good policy
Boy/Male
Indian, Punjabi, Sikh
King
Boy/Male
Arabic, Muslim, Parsi
Possessor of the World
Boy/Male
Hindu
Servant of dwarka
Boy/Male
Tamil
Shaistakhan | ஷைஸà¯à®¤à®¾à®•à®¾à®¨
Polite
SPIN GROUP
SPIN GROUP
SPIN GROUP
SPIN GROUP
SPIN GROUP
a.
Like a spine in shape; slender.
v. t.
To draw out, and twist into threads, either by the hand or machinery; as, to spin wool, cotton, or flax; to spin goat's hair; to produce by drawing out and twisting a fibrous material.
imp. & p. p.
of Spin
v. i.
To move swifty; as, to spin along the road in a carriage, on a bicycle, etc.
n.
A sin offering; a sacrifice for sin.
v. i.
To practice spinning; to work at drawing and twisting threads; to make yarn or thread from fiber; as, the woman knows how to spin; a machine or jenny spins with great exactness.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
n.
The act of spinning; as, the spin of a top; a spin a bicycle.
v. t.
To cause to turn round rapidly; to whirl; to twirl; as, to spin a top.
v. t.
To protract; to spend by delays; as, to spin out the day in idleness.
v. t.
To draw out tediously; to form by a slow process, or by degrees; to extend to a great length; -- with out; as, to spin out large volumes on a subject.
v. i.
To attend to a spit; to use a spit.
imp.
of Spin
a.
Full of spines; thorny; as, a spiny tree.
v. t.
To measure by the span of the hand with the fingers extended, or with the fingers encompassing the object; as, to span a space or distance; to span a cylinder.
v. t.
To cover with skin, or as with skin; hence, to cover superficially.
v. t.
To strip off the skin or hide of; to flay; to peel; as, to skin an animal.
imp. & p. p.
of Spit