Blackbox computation of $A_\infty$-algebras

$L_\infty$-structure on Barzdell's complex for monomial algebras

Let $A$ be a monomial associative finite dimensional algebra over a field $\Bbbk$ of characteristic zero. It is well known that the Hochschild cohomology of $A$ can be computed using Bardzell's complex $B(A)$. The aim of this article is to describe an explict $L_\infty$-structure on $B(A)$ that induces a weak equivalence of $L_\infty$-algebras between $B(A)$ and the Hochschild complex $C(A)$ of $A$. This allows us to describe the Maurer-Cartan equation in terms of elements of degree $2$ in $B(A)$. Finally, we make concrete computations when $A$ is a truncated algebra, and we prove that Bardzel…

$A_{\infty}$-结构在有限群代数Tate-Hochschild上同调加法分解中的研究

$A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra

本文研究了有限群代数的Tate-Hochschild上同调的加法分解中的$A_{\infty}$-结构，提供了计算框架和显式乘法公式。