Hochschild cohomology of twisted tensor products
Hochschild cohomology of twisted tensor products
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DOI：
10.1007/s00209-021-02949-7
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发表时间：
2020-05
影响因子：
0.8
通讯作者：
Benjamin Briggs;S. Witherspoon
中科院分区：
文献类型：
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作者：
Benjamin Briggs;S. Witherspoon
两个代数的张量积的乘法可以用一个双特征变形，得到一个扭曲的张量积。我们完全描述的Hochschild上同调的分量RandS的Hochschild上同调，包括完整的Gerstenhaber代数结构。这种描述推广了Bergh和Oppermann的一个结果。一些有趣的非交换代数类以双特征扭曲张量积的形式出现，有时是以不明显的方式。主要结果，从而使我们能够显着简化各种计算在文献中，并计算Hochschild上同调在几个新的类的例子。特别地，我们完全计算量子完全交代数的Hochschild上同调，任意数量的不定。一个新的工具，其中进入主要定理是轨道Hochschild上同调，这可以定义为代数与群作用，并满足扭曲版本的通常Gerstenhaber代数公理。
The tensor productof two algebras can have its multiplication deformed by a bicharacter to yield a twisted tensor product. We completely describe the Hochschild cohomology ofin terms of the Hochschild cohomology of the componentsRandS, including the full Gerstenhaber algebra structure. This description generalizes a result of Bergh and Oppermann. A number of interesting classes of noncommutative algebras arise as bicharacter twisted tensor products, sometimes in non-obvious ways. The main result thereby allows us to significantly simplify various calculations in the literature, and to compute Hochschild cohomology in several new classes of examples. In particular, we fully compute the Hochschild cohomology of quantum complete intersection algebras, with any number of indeterminates. One new tool which goes into the main theorem is orbit Hochschild cohomology, which can be defined for algebras with a group action, and which satisfies twisted versions of the usual Gerstenhaber algebra axioms.