$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
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DOI：
10.4171/jncg/372
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发表时间：
2018-05
影响因子：
0.9
通讯作者：
C. Negron;Y. Volkov;S. Witherspoon
中科院分区：
文献类型：
--
作者：
C. Negron;Y. Volkov;S. Witherspoon
我们证明了域上代数的Hochschild上同调是该代数的任意射影双模分解上的无限上导子空间。Gertenhaber括号是无穷个上导子的分次交换子。因此，我们将Stasheff关于Hochschild上同调的Gertenhaber括号的实现推广到任意分辨率，作为代数的张量余代数上的上导子的分次交换子。
We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. We thus generalize, to an arbitrary resolution, Stasheff's realization of the Gerstenhaber bracket on Hochschild cohomology as the graded commutator of coderivations on the tensor coalgebra of the algebra.