Homotopy liftings and Hochschild cohomology of some twisted tensor products
Homotopy liftings and Hochschild cohomology of some twisted tensor products
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DOI：
10.1142/s0219498822502383
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发表时间：
2020-05
影响因子：
0.8
通讯作者：
Pablo S. Ocal;Tolulope Nathaneal Oke;S. Witherspoon
中科院分区：
文献类型：
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作者：
Pablo S. Ocal;Tolulope Nathaneal Oke;S. Witherspoon
代数的张量积的Hochschild上同调同构于Hochschild上同调代数的分次张量积，即Gertenhaber代数。当张量积被双特征线扭曲时，类似的结果也成立。我们利用Volkov同伦提升给出了这些同构的新证明，这些提升是为了处理任意双模分解上的Gertenhaber括号而引入的。我们的结果说明了同伦提升在理论上的用途。
The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We present new proofs of these isomorphisms, using Volkov’s homotopy liftings that were introduced for handling Gerstenhaber brackets expressed on arbitrary bimodule resolutions. Our results illustrate the utility of homotopy liftings for theoretical purposes.