dorsal/arxiv
View SchemaMultibraces on the Hochschild complex
| Authors | Fusun Akman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9702010 |
| URL | https://arxiv.org/abs/q-alg/9702010 |
Abstract
We generalize the coupled braces {x}{y} of Gerstenhaber and {x}{y,...,z} of Getzler depicting compositions of multilinear maps in the Hochschild complex C(A)=Hom(TA;A) of a graded vector space A to expressions of the form {x,...,y}...{z,...,w} on the extended space Hom(TA;TA), and clarify many of the existing sign conventions that show up in the algebra of mathematical physics (namely in associative and Lie algebras, Batalin-Vilkovisky algebras, homotopy associative and homotopy Lie algebras). As a result, we introduce a new variant of the master identity for homotopy Lie algebras. We also comment on the bialgebra cohomology differential of Gerstenhaber and Schack, and define multilinear higher order differential operators with respect to multilinear maps using the new language. The continuation of this work will be on the various homotopy structures on a topological vertex operator algebra, as introduced by Kimura, Voronov, and Zuckerman.
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"abstract": "We generalize the coupled braces {x}{y} of Gerstenhaber and {x}{y,...,z} of\nGetzler depicting compositions of multilinear maps in the Hochschild complex\nC(A)=Hom(TA;A) of a graded vector space A to expressions of the form\n{x,...,y}...{z,...,w} on the extended space Hom(TA;TA), and clarify many of the\nexisting sign conventions that show up in the algebra of mathematical physics\n(namely in associative and Lie algebras, Batalin-Vilkovisky algebras, homotopy\nassociative and homotopy Lie algebras). As a result, we introduce a new variant\nof the master identity for homotopy Lie algebras. We also comment on the\nbialgebra cohomology differential of Gerstenhaber and Schack, and define\nmultilinear higher order differential operators with respect to multilinear\nmaps using the new language. The continuation of this work will be on the\nvarious homotopy structures on a topological vertex operator algebra, as\nintroduced by Kimura, Voronov, and Zuckerman.",
"arxiv_id": "q-alg/9702010",
"authors": [
"Fusun Akman"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Multibraces on the Hochschild complex",
"url": "https://arxiv.org/abs/q-alg/9702010"
},
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