Exact sequences, Hochschild cohomology, and the Lie module structure over the M-relative center

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• 作者：Reiner Hermann ^{reiner.hermann@math.ntnu.no" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16E40 ; secondary ; 14F35 ; 18D10 ; 18E10 ; 18G15
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：454
• 期：Complete
• 页码：29-69
• 全文大小：622 K

文摘

In this article, we present actions by central elements on Hochschild cohomology groups with arbitrary bimodule coefficients, as well as an interpretation of these actions in terms of exact sequences. Since our construction utilizes the monoidal structure that the category of bimodules possesses, we will further recognize that these actions are compatible with monoidal functors and thus, as a consequence, are invariant under Morita equivalences. By specializing the bimodule coefficients to the underlying algebra itself, our efforts in particular yield a description of the degree-(n,0)$(n,0)$-part of the Lie bracket in Hochschild cohomology, and thereby close a gap in earlier work by S. Schwede.