This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Lie operad" – news · newspapers · books · scholar · JSTOR(May 2024)
This article includes inline citations, but they are not properly formatted. Please improve this article by correcting them.(May 2024) (Learn how and when to remove this message)
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) in their formulation of Koszul duality.
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 Lieoperad is an operad whose algebras are Lie algebras. The notion (at least one version) was introduced by Ginzburg & Kapranov (1994)...
are Lie algebras. The quadratic duality mentioned above is such that the associative operad is self-dual, while the commutative and the Lieoperad correspond...
related to the free Lie algebra on the components of the link, as discussed in that article. See also Lieoperad 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 Lieoperad" (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...
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...
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...
Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced by Huang, Kriz, and others, D-module-theoretic objects...
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...
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...
Eilenberg, Homological algebra Fresse, Benoit (21 April 2017). Homotopy of Operads and Grothendieck-Teichmuller Groups. Mathematical Surveys and Monographs...
a structure that behaves like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Differential algebra Free algebra Geometric...
(1998). "Lie groups and p-compact groups". Proceedings of the International Congress of Mathematicians. Vol. 2. pp. 433–442. "Introduction to Operads (William...
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...
21, 1996). "The Pre-History Of Operads". In Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.). Operads: Proceedings of Renaissance Conferences...
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....
diagrammatic formalism of algebras which is described in Algebra+Homotopy=Operad explaining how to visually think about this higher homotopies. This intuition...
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...
(1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings...
"Grothendieck–Teichmüller groups", Grothendieck–Teichmüller Groups, Deformation and Operads, archived from the original on 2014-03-09, retrieved 2014-01-02 Schneps...
monograph on foliations and Lie groupoids. Recently Moerdijk pursues, among other topics, research on the theory of operads, on the logic structure of...
only finitely many cells in each dimension. operad The portmanteau of “operations” and “monad”. See operad. orbibundle orbibundle. orbit category orientation...
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...
Global Information
