Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions
Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions
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DOI：
10.2140/pjm.2016.283.223
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发表时间：
2014-05
影响因子：
0.6
通讯作者：
S. Witherspoon;Guodong Zhou
中科院分区：
文献类型：
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作者：
S. Witherspoon;Guodong Zhou
我们构造了量子对称代数(斜多项式环)的bar和Koszul分辨率之间的链映射。这种构造使用一种递归技术，涉及收缩同伦的显式公式。我们使用这些链映射来计算Gertenhaber括号，得到对称代数(多项式环)上Schouten-Nijenhuis括号的量子版本。在某些情况下，我们还计算了作为量子对称代数的群扩张而产生的斜群代数的括号。
We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute brackets also in some cases for skew group algebras arising as group extensions of quantum symmetric algebras.