1997/02/07 by Füsun Akman, Fusun Akman, Akman, Fusun
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #hep-th #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9702010
38 pages, LaTeX three times. Enlarged introduction, minor corrections
openalex publication_date 1997/02/07 · arxiv created 1997/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the coupled braces xy of Gerstenhaber and xy,...,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.