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


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.)


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.


Hochschild cohomology, deformation of algebras

2010 Mathematics Subject Classification

Primary 16E40. Secondary 16S80.

Published 18 May 2015