论文标题
Hochschild共同学的分级编织的通勤性
Graded braided commutativity in Hochschild cohomology
论文作者
论文摘要
我们证明了$ a $ a $ a $ a $ a a $ a $ a $ a $是YETTER-DRINFELD模块的编织型Hopf代数的hochschild共同体的分级编织的构成构成的通勤性。这是Mastnak，Pevtsova，Schauenburg和Witherspoon对结果的概括，其中包括Nichols代数，例如Jordan和Super Jordan Plane。我们通过在$ a $ a-bimodules的链条复合物的综合类别中的上述投影分辨率上构建了一个相关的射击结构，从而证明了这一结果。我们还证明，在任意编织的单体类别中，编织的双子币$ a $的Hochschild综合体是一种与脱谐的共同体，可诱导Hochschild cop产品的同型共同体。
We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of $A$ as $A$-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of $A$-bimodules. We also prove that the Hochschild complex of a braided bialgebra $A$ in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.
