论文标题
较高的环状霍基柴尔德共同体学上的卡拉比YAU代数和非交通分节
Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology
论文作者
论文摘要
我们证明了$ l _ {\ infty} $ - 较高的循环hochschild complex $ \ chh $的形式超过了Quiver的免费联想代数或路径代数。 $ \ chh $复合物是作为定义前卡比YAU结构的适当工具引入的。我们表明，在自由代数（路径代数）的情况下，该复合物的共同体是纯净的，该代数集中在零度上。它是形式证明的主要成分。对于任何平滑的代数，我们选择一个较高的循环hochschild综合体中的小QISO子复合物，这会产生高度非共同单位的计算，我们称它们为$ξδ$ - 工程学。该子复合物上的谎言结构是用$ξδ$ - 工程学的组合描述的。该子复合件和$ξδ$ - 工程学的基础与Groebner Bases理论的参数相结合，用于较高环状Hochschild复合体的共同体学计算。特别是$ξδ$ - 工程学的语言允许将前 - YAU结构解释为一种非共同的泊松结构。
We prove $L_{\infty}$-formality for the higher cyclic Hochschild complex $\chH$ over free associative algebra or path algebra of a quiver. The $\chH$ complex is introduced as an appropriate tool for the definition of pre-Calabi-Yau structure. We show that cohomologies of this complex are pure in case of free algebras (path algebras), concentrated in degree zero. It serves as a main ingredient for the formality proof. For any smooth algebra we choose a small qiso subcomplex in the higher cyclic Hochschild complex, which gives rise to a calculus of highly noncommutative monomials, we call them $ξδ$-monomials. The Lie structure on this subcomplex is combinatorially described in terms of $ξδ$-monomials. This subcomplex and a basis of $ξδ$-monomials in combination with arguments from Groebner bases theory serves for the cohomology calculations of the higher cyclic Hochschild complex. The language of $ξδ$-monomials in particular allows an interpretation of pre-Calabi-Yau structure as a noncommutative Poisson structure.
