论文标题
Fomin-Kirillov代数的Hochschild共同学上的Gerstenhaber结构
Gerstenhaber structure on Hochschild cohomology of the Fomin-Kirillov algebra on 3 generators
论文作者
论文摘要
本文的目的是计算Fomin-Kirillov代数的Hochschild共同体的Gerstenhaber括号，这是在三个发电机上的特征领域，不同于$ 2 $和3美元。这部分是基于一种一般方法，我们介绍以轻松计算$ \ permatorName {hh}^{0} $的元素之间的gerstenhaber括号与$ \ operatotorname {hh}^{hh}^{n}（n}（n}（n}（a）$ n \ in \ mathbb in \ mathbb in \ n n n} by su s su su su su s su su {0计算$ \ operatorName {hh}^{1}（a）元素之间的gerstenhaber括号，以及$ \ operatorAtorName {hh}^{n}^{n}（a）$的$ n \ in \ in \ mathbb {n} _ {0} $，以及以前的comptute conconte conconter conconte re conconte conconte conconte consement。我们还表明，$ \ operatorname {hh}^{\ bullet}（a）$的Gerstenhaber支架不会由任何Batalin-Vilkovisky Generator诱导。
The goal of this article is to compute the Gerstenhaber bracket of the Hochschild cohomology of the Fomin-Kirillov algebra on three generators over a field of characteristic different from $2$ and $3$. This is in part based on a general method we introduce to easily compute the Gerstenhaber bracket between elements of $\operatorname{HH}^{0}(A)$ and elements of $\operatorname{HH}^{n}(A)$ for $n \in \mathbb{N}_{0}$, the method by M. Suárez-Álvarez to calculate the Gerstenhaber bracket between elements of $\operatorname{HH}^{1}(A)$ and elements of $\operatorname{HH}^{n}(A)$ for any $n \in \mathbb{N}_{0}$, as well as an elementary result that allows to compute the remaining brackets from the previous ones. We also show that the Gerstenhaber bracket of $\operatorname{HH}^{\bullet}(A)$ is not induced by any Batalin-Vilkovisky generator.
