Cohomology of twisted tensor products

JOURNAL OF ALGEBRA

卷:320

Article

Bergh, Petter Andreas¹  Oppermann, Steffen¹ 

[1] NTNU, Inst Matemat Fag, N-7491 Trondheim, Norway

关键词: twisted tensor products;    Hochschild cohomology;    quantum complete intersections;    representation dimension;   

DOI  :  10.1016/j.jalgebra.2008.08.005

来源: Elsevier

【 摘 要 】

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this is still true. We give an explicit description of the Ext-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential part of the Hochschild cohomology ring of a twisted tensor product. As an application. we characterize precisely when the cohomology groups over a quantum complete intersection are finitely generated over the Hochschild cohomology ring. Moreover, both for quantum complete intersections and in related cases we obtain a lower bound for the representation dimension of the algebra. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free