Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Operations on the secondary Hochschild cohomology

Pages: 129 – 146

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n1.a6

Authors

Mihai D. Staic (Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio, U.S.A.; and Institute of Mathematics of the Romanian Academy, Bucharest, Romania)

Alin Stancu (Department of Mathematics, Columbus State University, Columbus, Georgia, U.S.A.)

Abstract

We show that the secondary Hochschild cohomology associated to a triple $(A,B, \epsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove that the total secondary Hochschild complex is a multiplicative nonsymmetric operad, discuss the connection with extensions of $B$-algebras, and give a Hodge-type decomposition of the secondary Hochschild cohomology.

Keywords

Hochschild cohomology, deformation of algebras

2010 Mathematics Subject Classification

Primary 16E40. Secondary 16S80.

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Published 18 May 2015