Searches , social queries for ELLIPTIC ALGEBRA
Search references for ELLIPTIC ALGEBRA. Phrases containing ELLIPTIC ALGEBRA
See searches and references containing ELLIPTIC ALGEBRA!
Search references for ELLIPTIC ALGEBRA. Phrases containing ELLIPTIC ALGEBRA
See searches and references containing ELLIPTIC ALGEBRA!ELLIPTIC ALGEBRA
In algebra, an elliptic algebra is a certain regular algebra of a Gelfand–Kirillov dimension three (quantum polynomial ring in three variables) that corresponds
Elliptic_algebra
Algebraic curve in mathematics
mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined
Elliptic_curve
Non-Euclidean geometry
produce 3D vector space and elliptic space, respectively. Access to elliptic space structure is provided through the vector algebra of William Rowan Hamilton:
Elliptic_geometry
Approach to public-key cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC
Elliptic-curve_cryptography
Type of surface singularity used in algebraic geometry
In algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic
Elliptic_singularity
Mathematical concept
be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular. There are many different but
Supersingular_elliptic_curve
Branch of mathematics
most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves
Algebraic_geometry
Algebraic variety with a group structure
Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties
Algebraic_group
Special function defined by an integral
Legendre's trigonometric form of the elliptic integral; substituting t = sin θ and x = sin φ, one obtains Jacobi's algebraic form: F ( x ; k ) = ∫ 0 x d t (
Elliptic_integral
Mathematical concept
mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such
Elliptic_surface
Mathematical structure in abstract algebra
mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of
*-algebra
theorem Elliptic surface Surface of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Estimates the number of points on an elliptic curve over a finite field
function field associated with the elliptic curve. A generalization of the Hasse bound to higher genus algebraic curves is the Hasse–Weil bound. This
Hasse's theorem on elliptic curves
Hasse's_theorem_on_elliptic_curves
Mathematical object studied in the field of algebraic geometry
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as
Algebraic_variety
Topics referred to by the same term
mathematics, Hasse invariant may refer to: Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form This disambiguation
Hasse_invariant
Mathematical theory of topological spaces
(isomorphism classes of) certain algebraic objects called Sullivan minimal models, which are commutative differential graded algebras over the rational numbers
Rational_homotopy_theory
1995 publication in mathematics
two manuscripts, "Modular elliptic curves and Fermat's Last Theorem" and "Ring theoretic properties of certain Hecke algebras", the second of which Wiles
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Group of real 2×2 matrices with unit determinant
geometry. The group SL(2, R) acts on its Lie algebra sl(2, R) by conjugation (remember that the Lie algebra elements are also 2 × 2 matrices), yielding
SL2(R)
Quaternion of norm 1 (unit quaternion)
{r} ^{2}=-1\ } means that r {\displaystyle \ \mathbf {r} \ } is an algebraic imaginary unit. There is a sphere of imaginary units in the quaternions
Versor
Curve defined as zeros of polynomials
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in
Algebraic_curve
Class of periodic mathematical functions
{\displaystyle G_{6}} are so called Eisenstein series. In algebraic language, the field of elliptic functions is isomorphic to the field C ( X ) [ Y ] / (
Elliptic_function
Type of vector space
algebra is the algebra generated by Hecke operators, which are named after Erich Hecke. The algebra is a commutative ring. In the classical elliptic modular
Hecke_algebra
Branch of algebraic geometry
mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered
Arithmetic_geometry
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Projective variety that is also an algebraic group
varieties of other algebraic varieties. The group law of an abelian variety is necessarily commutative and the variety is non-singular. An elliptic curve is an
Abelian_variety
Mathematical curves that are isomorphic over algebraic closures
mathematical field of algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic
Twists_of_elliptic_curves
Modular function in mathematics
of elliptic curves over the complex numbers, or more generally, an algebraically closed field. Over other fields there exist examples of elliptic curves
J-invariant
Computer system for solving algebra problems
include the Elliptic Curve Method, the Quadratic sieve and the Number field sieve. Algebraic number theory Magma includes the KANT computer algebra system
Magma (computer algebra system)
Magma_(computer_algebra_system)
commutative graded ring. Elliptic algebra Calabi–Yau algebra Sklyanin algebra Ajitabh, Kaushal (1994), Modules over regular algebras and quantum planes (PDF)
Noncommutative projective geometry
Noncommutative_projective_geometry
mathematics and related fields. Iwahori–Hecke algebra Quantum affine algebra Quantum enveloping algebra Quantum group Jackson integral q-derivative q-difference
List_of_q-analogs
Elements taken to zero by a homomorphism
In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism
Kernel_(algebra)
Generalization of a scheme
numbers by a lattice is an algebraic space, but is not an elliptic curve, even though the corresponding analytic space is an elliptic curve (or more precisely
Algebraic_space
Lie group of Lorentz transformations
group on Minkowski space uses biquaternions, which form a composition algebra. The isometry property of Lorentz transformations holds according to the
Lorentz_group
Algebra describing 2D conformal symmetry
mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional
Virasoro_algebra
Class of mathematical functions
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This
Weierstrass_elliptic_function
Awarded every year by the American Mathematical Society
ISBN 9780821853368. Eisenbud, David (1995). Commutative Algebra with a View Toward Algebraic Geometry. Graduate Texts in Mathematics. Vol. 150. Springer
Leroy_P._Steele_Prize
specifically the field of algebra, Sklyanin algebras are a class of noncommutative algebra named after Evgeny Sklyanin. This class of algebras was first studied
Sklyanin_algebra
Cone with an elliptical base
An elliptical cone is a cone with an elliptical base. It is a generalization of the circular cone and a special case of the generalized cone. The term
Elliptic_cone
Theory of a class of elliptic curves
definite quaternion algebra over Q. When the field of definition is a finite field, there are always non-trivial endomorphisms of an elliptic curve, coming
Complex_multiplication
Two geometries based on axioms closely related to those specifying Euclidean geometry
metric geometry. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When isotropic quadratic
Non-Euclidean_geometry
Concept in mathematics
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal
Universal_enveloping_algebra
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Type of mathematical function
algebraic function, such as the error function and the elliptic integrals, were elementary functions of the second kind; their inverses, the elliptic
Elementary_function
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
Algebraic variety
complex algebraic manifold, since it is the complex projective line. Compact Riemann surfaces Riemann sphere Elliptic curves Grassmannian Algebraic geometry
Algebraic_manifold
Type of map between algebraic groups
In mathematics, particularly in algebraic geometry, an isogeny between two abelian varieties is a surjective homormophism with a finite kernel. In the
Isogeny
Conjecture in number theory
William; Stoll, Michael (2023). "Torsion points on elliptic curves over number fields of small degree". Algebra & Number Theory. 17 (2): 267–308. arXiv:1707
Torsion_conjecture
Number in {..., –2, –1, 0, 1, 2, ...}
numbers. In algebraic number theory, integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In
Integer
Algorithm for integer factorization
general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra. It is an algebraic-group factorisation algorithm. Practically
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
mathematics, a hyperelliptic surface, or bi-elliptic surface, is a minimal surface whose Albanese morphism is an elliptic fibration without singular fibres. Any
Hyperelliptic_surface
method. If the algebraic group is an elliptic curve, the one-sided identities can be recognised by failure of inversion in the elliptic-curve point addition
Algebraic-group factorization algorithm
Algebraic-group_factorization_algorithm
Quantum consistency equation
trigonometric and elliptic. These are related to quantum groups known as the Yangian, affine quantum groups and elliptic algebras respectively. Set-theoretic
Yang–Baxter_equation
One-dimensional complex manifold
containing no such points). This is an example of an algebraic curve. Every elliptic curve is an algebraic curve, given by (the compactification of) the locus
Riemann_surface
Algebraic structure with addition, multiplication, and division
operations on rational numbers do. Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Mathematical classification of surfaces
are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic. The algebraic ones are
Enriques–Kodaira classification
Enriques–Kodaira_classification
Number of independent rational basis points with infinite order
In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational
Rank_of_an_elliptic_curve
Algebraic invariant of topological spaces
In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms. Historically
Elliptic_cohomology
Geometric space
In algebraic geometry, a moduli space of curves is a space whose points correspond to isomorphism classes of algebraic curves. The term "modulus" was
Moduli_of_algebraic_curves
On properties of Galois representations associated with modular forms
Ribet's theorem shows that if the Galois representation associated with an elliptic curve has certain properties, then that curve cannot be modular (in the
Ribet's_theorem
Elliptic curves
Hodge-Arakelov theory of elliptic curves. I", in Fried, Michael D.; Ihara, Yasutaka (eds.), Arithmetic fundamental groups and noncommutative algebra (Berkeley, CA
Hodge–Arakelov_theory
French mathematician (born 1926)
French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in
Jean-Pierre_Serre
36 mathematical problems stated in 1955
problems primarily focused on algebraic geometry, number theory, and the connections between modular forms and elliptic curves. Taniyama's twelfth and
Taniyama's_problems
German mathematician (1804–1851)
arbitrary algebraic curves, may be seen as a higher genus generalization of the relation between elliptic integrals and the Jacobi or Weierstrass elliptic functions
Carl_Gustav_Jacob_Jacobi
Concept in mathematics
additive and multiplicative algebraic groups. Another important special case of this is the formal group (law) of an elliptic curve (or abelian variety)
Formal_group_law
Topics referred to by the same term
parameter in elliptic curve cryptography, defined as the ratio between the order of a group and that of the subgroup Cofactor (linear algebra), the signed
Cofactor
Group of unitary complex matrices with determinant of 1
Lie algebra s u ( n ) {\displaystyle {\mathfrak {su}}(n)} of SU(n) consists of n × n skew-Hermitian matrices with trace zero. This (real) Lie algebra has
Special_unitary_group
Prime number with a certain relationship to an elliptic curve
In algebraic number theory, a supersingular prime for a given elliptic curve is a prime number with a certain relationship to that curve. If the curve
Supersingular prime (algebraic number theory)
Supersingular_prime_(algebraic_number_theory)
248-dimensional exceptional simple Lie group
several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding
E8_(mathematics)
Algebraic stack in mathematics
elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M e l l {\displaystyle {\mathcal {M}}_{\mathrm {ell} }} , is an algebraic
Moduli stack of elliptic curves
Moduli_stack_of_elliptic_curves
French mathematician (1540–1603)
Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters
François_Viète
Group that is also a differentiable manifold with group operations that are smooth
circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation
Lie_group
In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding
Level structure (algebraic geometry)
Level_structure_(algebraic_geometry)
Signal processing filter
the elliptic rational function. ζ n {\displaystyle \zeta _{n}} is expressible for all n in terms of Jacobi elliptic functions, or algebraically for some
Elliptic_filter
Mathematical concept
supersingular elliptic curves over the algebraic closure of Fp, and all such j-invariants lie in Fp2. The first example of a supersingular elliptic curve was
Supersingular_variety
Gauss sum on an elliptic curve
degree 1 Asai, Tetsuya (2007), "Elliptic Gauss sums and Hecke L-values at s = 1", Proceedings of the Symposium on Algebraic Number Theory and Related Topics
Elliptic_Gauss_sum
Branch of mathematics that studies the properties of groups
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known
Group_theory
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Mathematician
connected algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and
Vladimir_Drinfeld
American mathematician (born 1934)
of Technology Mathematics Department, known for his contributions to algebraic geometry. Artin was born in Hamburg, Germany, and brought up in Indiana
Michael_Artin
Plane curve
elongation, no longer an ellipse but a parabola). An ellipse has a simple algebraic formula for its area, but for its perimeter (also known as circumference)
Ellipse
Generalization of covers
the corresponding projective elliptic curve to the projective line. The previous example may be generalized to any algebraic plane curve in the following
Branched_covering
American mathematician (born 1955)
exciting areas of algebraic geometry and number theory.” Silverman has also written four undergraduate texts: Rational Points on Elliptic Curves (1992, co-authored
Joseph_H._Silverman
17th-century conjecture proved by Andrew Wiles in 1994
two manuscripts, "Modular elliptic curves and Fermat's Last Theorem" and "Ring theoretic properties of certain Hecke algebras", the second of which was
Fermat's_Last_Theorem
Mathematical functions that quantify complexity
equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the classical
Height_function
Topics referred to by the same term
of an elliptic operator Regularity theory of elliptic partial differential equations Regular algebra, or Kleene algebra Regular code, an algebraic code
Regular
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Unsolved problem in geometry
unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties
Hodge_conjecture
Monster and modular connection
Tachikawa observed that the elliptic genus of a K3 surface can be decomposed into characters of the N = (4,4) superconformal algebra, such that the multiplicities
Monstrous_moonshine
Riemannian manifold with SU(n) holonomy
A one-dimensional Calabi–Yau manifold is a complex elliptic curve, and in particular, algebraic. In two complex dimensions, the K3 surfaces furnish the
Calabi–Yau_manifold
Group of flat spacetime symmetries
{Spin} (1,3)} . The Poincaré algebra is the Lie algebra of the Poincaré group. It is a Lie algebra extension of the Lie algebra of the Lorentz group. More
Poincaré_group
American mathematician
studies, among other things, étale homotopy theory, elliptic surfaces, computer-based algebraic geometry (such as Gröbner basis), Torelli sets and toric
David_A._Cox
Algebraic variety in a projective space
In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in
Projective_variety
Type of smooth complex surface of kodaira dimension 0
identically zero. The proof uses that an algebraic K3 surface X is always covered by a continuous family of images of elliptic curves. (These curves are singular
K3_surface
Unproved conjecture in mathematics
conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Branch of mathematics
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Generalization of algebraic spaces or schemes
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli
Algebraic_stack
Branch of mathematics
of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a
Geometry
Type of mathematical object
from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups
Group_scheme
Mathematical result in differential geometry
by the Grothendieck group of algebraic vector bundles. Due to (Teleman 1983), (Teleman 1984): For any abstract elliptic operator (Atiyah 1970) on a closed
Atiyah–Singer_index_theorem
Mathematical concept
A modular elliptic curve is an elliptic curve E that admits a parametrization X0(N) → E by a modular curve. This is not the same as a modular curve that
Modular_elliptic_curve
travel, tourism, insurance
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
ELLIPTIC ALGEBRA
travel, tourism, insurance