论文标题
$ l_ \ infty $ - 在Barzdell的单一代数的综合体上的结构
$L_\infty$-structure on Barzdell's complex for monomial algebras
论文作者
论文摘要
让$ a $为特征零的字段$ \ bbbk $上的单一协会有限维数。众所周知，可以使用Bardzell的Complex $ b（a）$计算$ a $的Hochschild共同体。本文的目的是描述$ b（a）$上的解释$ l_ \ infty $ - 结构，该结构在$ b（a）$和hochschild complect $ c（a）$ c（a）$ a $ a $之间引起$ l_ \ infty $ -algebras的弱等效性。这使我们能够用$ 2 $ in $ b（a）$的$ 2 $的元素来描述毛勒 - 卡丹方程。最后，当$ a $是截短的代数时，我们进行具体的计算，我们证明Bardzell对激进平方零代数的综合体实际上是DG-Lie代数。
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 Bardzell's complex for radical square zero algebras is in fact a dg-Lie algebra.
