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Generalization of associativity properties
operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group actions. Operads originate in algebraic topology;
Operad
In mathematics, the Lie operad is an operad whose algebras are Lie algebras. The notion (at least one version) was introduced by Ginzburg & Kapranov (1994)
Lie_operad
Various mathematical dualites
commutative operad are commutative algebras, i.e., commutative (possibly graded, differential graded) rings. Yet another example is the Lie operad whose algebras
Koszul_duality
algebra, an operad algebra is an "algebra" over an operad. It is a generalization of an associative algebra over a commutative ring R, with an operad replacing
Operad_algebra
Algebraic structure used in analysis
of a Lie algebra Leibniz algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle
Lie_algebra
related to the free Lie algebra on the components of the link, as discussed in that article. See also Lie operad for the use of a free Lie algebra in the construction
Free_Lie_algebra
a homotopy algebra using the theory of operads: that is, a homotopy Lie algebra is an algebra over an operad in the category of chain complexes over
Homotopy_Lie_algebra
Sum of terms, each multiplied with a scalar
basic operations are a generating set for the operad of all linear combinations. Ultimately, this fact lies at the heart of the usefulness of linear combinations
Linear_combination
Type of mathematical category
sets and bijections between them. Trimble n.d., § 1 Trimble, Todd H. "Notes on the Lie operad" (PDF). University of Chicago. Retrieved 2022-09-27. v t e
Permutation_category
Mathematical condition
Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and Deligne's conjecture". Conférence Moshé Flato 1999: Quantization, Deformations
Poincaré_lemma
the generators. Chapoton, F.; Livernet, M. (2001), "Pre-Lie algebras and the rooted trees operad", International Mathematics Research Notices, 2001 (8):
Pre-Lie_algebra
American mathematician (Jon Peter May; born 1939)
in particular, for the May spectral sequence and for coining the term operad. May received a Bachelor of Arts degree from Swarthmore College in 1960
J._Peter_May
Algebraic structure in homological algebra
Deformation Theory. I (PDF) Loday, Jean-Louis; Vallette, Bruno (2012), Algebraic Operads, Grundlehren der mathematischen Wissenschaften, vol. 346, Heidelberg, New
Differential_graded_algebra
Algebra used in 2D conformal field theories and string theory
Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced by Huang, Kriz, and others, D-module-theoretic objects
Vertex_operator_algebra
American mathematician
(1998). "Lie groups and p-compact groups". Proceedings of the International Congress of Mathematicians. Vol. 2. pp. 433–442. "Introduction to Operads (William
William_Gerard_Dwyer
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also References Operad theory a type of abstract algebra concerned with prototypical algebras.
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Theory of algebraic structures in general
finite products). A more recent development in category theory is operad theory – an operad is a set of operations, similar to a universal algebra, but restricted
Universal_algebra
S2CID 121944962. Ginzburg, V.; Kapranov, M. (1994). "Koszul duality for operads". Duke Math. J. 76: 203–273. arXiv:0709.1228. doi:10.1215/s0012-7094-94-07608-4
Leibniz_algebra
History of maths
21, 1996). "The Pre-History Of Operads". In Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.). Operads: Proceedings of Renaissance Conferences
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Kazakh mathematician and physicist (born 1956)
16–2013, art. 13.1.4 Dzhumadildaev A.S., Zusmanovich P., The alternative operad is not Koszul // Experimental Mathematics. – 2011. – V. 20, No.2. – P. 138–144
Askar_Dzhumadildayev
195–213. Ginzburg, Victor; Kapranov, Mikhail (1994). "Koszul duality for operads". Duke Mathematical Journal. 76: 203–273. arXiv:0709.1228. doi:10
Zinbiel_algebra
Frabetti, Alessandra; Goichot, François (eds.). Dialgebras and Related Operads. Lecture Notes in Mathematics. Vol. 1763. Springer. pp. 7–66. doi:10.1007/3-540-45328-8_2
Dialgebra
World Scientific. ISBN 9789814520430. Kontsevich, Maxim (1 April 1999). "Operads and Motives in Deformation Quantization". Letters in Mathematical Physics
Deformation_quantization
Vector space equipped with a bilinear product
a structure that behaves like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Composition algebra Differential algebra
Algebra_over_a_field
Series of advanced mathematics textbooks
martingale approximation. 2012 Jean-Louis Loday, Bruno Vallette: Algebraic Operads. 2012 Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke: Poisson Structures
Grundlehren der mathematischen Wissenschaften
Grundlehren_der_mathematischen_Wissenschaften
American mathematician
ideas leading to the theory of operads; homotopy theoretic approaches to Hilbert's fifth problem on the characterization of Lie groups; and the study of Poisson
Jim_Stasheff
Mathematical concept
Eilenberg, Homological algebra Fresse, Benoit (21 April 2017). Homotopy of Operads and Grothendieck-Teichmuller Groups. Mathematical Surveys and Monographs
Differential_graded_module
Polytope associated with combinatorial problems
(1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings
Cyclohedron
Theorem in category theory
ISSN 1076-9803. Loday, Jean-Louis; Vallette, Bruno (8 August 2012). Algebraic Operads. Grundlehren der mathematischen Wissenschaften. Vol. 346. Springer. doi:10
Mac_Lane's_coherence_theorem
Dutch mathematician
monograph on foliations and Lie groupoids. Recently Moerdijk pursues, among other topics, research on the theory of operads, on the logic structure of
Ieke_Moerdijk
Mathematician
(2020), whose dissertation was entitled Symmetric Homotopy Theory for Operads and Weak Lie 3-Algebras, Du Li (2014), whose dissertation was entitled Higher
Chenchang_Zhu
Branch of topology
of a cactus operad on the free loop space L M {\displaystyle LM} . The cactus operad is weakly equivalent to the framed little disks operad and its action
String_topology
Branch of mathematics
conjecture about affine space.) In this line of the approach, the notion of operad, a set or space of operations, becomes prominent: in the introduction to
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
French mathematician (1924–1987)
The concept of "analyseurs", reinvented by J. Peter May under the name operads. In 1958, Lazard was the first recipient of the Prix Audin, named after
Michel_Lazard
American mathematician and novelist
"Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads, archived from the original on 2014-03-09, retrieved 2014-01-02 Schneps
Leila_Schneps
Mathematics glossary
only finitely many cells in each dimension. operad The portmanteau of “operations” and “monad”. See operad. orbibundle orbibundle. orbit category orientation
Glossary of algebraic topology
Glossary_of_algebraic_topology
diagrammatic formalism of algebras which is described in Algebra+Homotopy=Operad explaining how to visually think about this higher homotopies. This intuition
Homotopy_associative_algebra
Alternative mathematical ordering
(1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings
Cyclic_order
Graduate-level textbooks in mathematics
Theory and Applications András Vasy 2015 978-1-4704-1881-6 170 Colored Operads Donald Yau 2016 978-1-4704-2723-8 171 Nonlinear Elliptic Equations of the
Graduate Studies in Mathematics
Graduate_Studies_in_Mathematics
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