Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Operations on the Hopf-Hochschild complex for module-algebras

Pages: 259 – 272

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n1.a10

Author

Donald Yau (Department of Mathematics, The Ohio State University, Newark, Ohio, U.S.A.)

Abstract

It is proved that Kaygun’s Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, an analogue of Deligne’s Conjecture holds for module-algebras, and the Hopf-Hochschild cohomology of a module-algebra has a Gerstenhaber algebra structure.

Keywords

module-algebra, Hopf-Hochschild cohomology, Gerstenhaber algebra, brace algebra, Deligne’s conjecture

2010 Mathematics Subject Classification

16E40

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Published 12 July 2011