Cohomology of twisted tensor products.
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Publication:958537
DOI10.1016/J.JALGEBRA.2008.08.005zbMATH Open1185.16012arXiv0803.3689OpenAlexW2025832665MaRDI QIDQ958537
Author name not available (Why is that?)
Publication date: 5 December 2008
Published in: (Search for Journal in Brave)
Abstract: 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 extend this is still true. We give an explicit description of the -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.
Full work available at URL: https://arxiv.org/abs/0803.3689
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