论文标题
莫里塔（Morita）无限变形的不变性
Morita invariance for infinitesimal deformations
论文作者
论文摘要
让$ a $和$ b $为两个字段$ \ bbbk $上的两个莫里塔等效的有限维数代数。众所周知，在莫里塔对等上，Hochschild的共同体是不变的。由于无穷小变形与第二个Hochschild共同学组连接，因此我们明确描述连接$ \ Mathsf {hh}^2（a）$的传输映射与$ \ Mathsf {hh}^2（b）$。这使我们能够将莫里塔等价转移到$ a $ a和$ b $之间的无限变形之间。作为一个应用程序，当$ \ bbbk $被代数关闭时，我们会考虑与$ a $相关的商路径代数，并描述Quiver的演示文稿以及$ a $的无限变形的关系。
Let $A$ and $B$ be two Morita equivalent finite dimensional associative algebras over a field $\Bbbk$. It is well known that Hochschild cohomology is invariant under Morita equivalence. Since infinitesimal deformations are connected with the second Hochschild cohomology group, we explicitly describe the transfer map connecting $\mathsf{HH}^2(A)$ with $\mathsf{HH}^2(B)$. This allows us to transfer Morita equivalence between $A$ and $B$ to that between infinitesimal deformations of them. As an application, when $\Bbbk$ is algebraically closed, we consider the quotient path algebra associated to $A$ and describe the presentation by quiver and relations of the infinitesimal deformations of $A$.
