operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group representations. Operads originate in algebraic topology;...

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)...

of a Lie algebra Leibniz algebra Lie algebra cohomology Lie algebra extension Lie algebra representation Lie bialgebra Lie coalgebra Lie operad Particle...

are Lie algebras. The quadratic duality mentioned above is such that the associative operad is self-dual, while the commutative and the Lie operad correspond...

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...

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...

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...

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...

the generators. Chapoton, F.; Livernet, M. (2001), "Pre-Lie algebras and the rooted trees operad", International Mathematics Research Notices, 2001 (8):...

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...

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...

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...

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...

Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced by Huang, Kriz, and others, D-module-theoretic objects...

World Scientific. ISBN 9789814520430. Kontsevich, Maxim (1 April 1999). "Operads and Motives in Deformation Quantization". Letters in Mathematical Physics...

Eilenberg, Homological algebra Fresse, Benoit (21 April 2017). Homotopy of Operads and Grothendieck-Teichmuller Groups. Mathematical Surveys and Monographs...

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...

Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and Deligne's conjecture". Conférence Moshé Flato 1999: Quantization, Deformations...

a structure that behaves like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Composition algebra Differential algebra...

(1998). "Lie groups and p-compact groups". Proceedings of the International Congress of Mathematicians. Vol. 2. pp. 433–442. "Introduction to Operads (William...

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....

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...

21, 1996). "The Pre-History Of Operads". In Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.). Operads: Proceedings of Renaissance Conferences...

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...

diagrammatic formalism of algebras which is described in Algebra+Homotopy=Operad explaining how to visually think about this higher homotopies. This intuition...

(1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings...

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...

only finitely many cells in each dimension. operad The portmanteau of “operations” and “monad”. See operad. orbibundle orbibundle. orbit category orientation...

195–213. Ginzburg, Victor; Kapranov, Mikhail (1994). "Koszul duality for operads". Duke Mathematical Journal. 76: 203–273. arXiv:0709.1228. doi:10...

and Applications, András Vasy (2015, ISBN 978-1-4704-1881-6) 170 Colored Operads, Donald Yau (2016, ISBN 978-1-4704-2723-8) 171 Nonlinear Elliptic Equations...