Operads in algebra, topology, and physics

By Martin Markl, S. Shnider, J. Stasheff. 2002

679 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/43c903a9d3b63d35d05cfa330c7aba349474dda4

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Citations in the corpus

Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras (2003, background): “, gn) satisfying associativity and unit [11].”
On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra (2003, background): “1 The suboperad generated by the brace operations It is well known ( [14,15,17] see also [33] for the history of the brace operations and Deligne’s conjecture) that the set of concatenations of multiplications and brace operations form a suboperad of the endomorphism operad of the Hochschild complex”
Coloured Koszul duality and strongly homotopy operads (2003, background): “For more extensive background on this and on (co)operads in general read GinzburgKapranov [3], Getzler-Jones [2], and Markl-Shnider-Stasheff [8].”
Homotopy Algebras Inspired by Classical Open-Closed String Field Theory (2004, background): “1 The relation (2.1) is diﬀerent from the original one [49] in the deﬁnition of the degrees of the multi-linear maps mk and hence of the signs. Both are in fact equivalent and related by desuspension [44]. In [49], the mk are multi-linear maps on ↓A where (↓A)r+1 = Ar; we denote desuspension by ↓. (”
An invitation to higher gauge theory (2010, background): “In fact, L∞-algebras were developed by Stasheff and collaborators [66,84] before higher gauge theory became recognized as a subject of study.”
Integrating $L_\infty $-algebras (2006, background): “Strongly homotopy associative monoids, also known as A∞-spaces (see [21][6][20]), are topological spaces M equipped with families of multiplication maps μn : Kn ×M n → M , where Kn are some contractible spaces.”
The topology of spaces of knots: cosimplicial models (2002, background): “The following is Theorem 4.19 of [43], and is well-known in different technical settings [37].”
Homology of generalized partition posets (2004, background): “perad. We give the examples of free and quadratic operads. 2.1.1. Deﬁnition. The survey of J.-L. Loday [L1] provides a good introduction to operads and the book of M. Markl, S. Shnider and J. Stasheﬀ [MSS] gives a full treatment of this notion. An algebraic operad is an algebraic object that models ”
On several varieties of cacti and their relations (2002, background): “lt; i+l (opk ◦i−l+1 op ′ l)◦j op ′′ m if i +l ≤j An operad morphism is a map of collections preserving all the operad structures. 1.1.7. Remark. Note that our operads correspond to the pseudooperadsof[MSS]. In case aunit exists these two notionscoincide [MSS]. We drop the “pseudo” in our nomenclatur”