On the Hochschild cohomology ring of tensor products of algebras |
| |
Authors: | Jue Le Guodong Zhou |
| |
Affiliation: | 1. School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, PR China;2. Department of Mathematics, East China Normal University, Dong Chuan Road 500, Min Hang District, Shanghai, 200241, PR China |
| |
Abstract: | We prove that, as Gerstenhaber algebras, the Hochschild cohomology ring of the tensor product of two algebras is isomorphic to the tensor product of the respective Hochschild cohomology rings of these two algebras, when at least one of them is finite dimensional. In case of finite dimensional symmetric algebras, this isomorphism is an isomorphism of Batalin–Vilkovisky algebras. As an application, we explain by examples how to compute the Batalin–Vilkovisky structure, in particular, the Gerstenhaber Lie bracket, over the Hochschild cohomology ring of the group algebra of a finite abelian group. |
| |
Keywords: | 16E40 |
本文献已被 ScienceDirect 等数据库收录! |
|