专家报告

题      目：Automorphisms of the category of free non-associative algebras with unit

报  告  人：Elena Aladova Chestakov 教授  (邀请人：张泽锐)

                                 巴西圣保罗大学

时      间：12月4日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

         Elena Aladova Chestakov is currently a postdoc at the University of São Paulo (Brasil). She has PhD in Algebra at Moscow Pedagogical State University (2004) and PhD in Computer Science at Bar-Ilan University (2019). Her main area of research is varieties and the theory of polynomial identities. Currently, she works mainly in the area of universal algebraic geometry.

摘      要：

       Let $\Theta$ be an arbitrary variety of algebras and $\Theta^{0}$ the category of all free finitely generated algebras in $\Theta$. The group $Aut(\Theta^{0})$ of automorphisms of the category $\Theta^{0}$ plays an important role in universal algebraic geometry. It turns out that for a wide class of varieties, the group $Aut(\Theta^{0})$ can be decomposed into a product of the normal subgroup $Inn(\Theta^{0})$ of inner automorphisms and the subgroup
$St(\Theta^{0})$ of strongly stable automorphisms. The method of verbal operations provides a machinery to calculate the group $St(\Theta^{0})$ of strongly stable automorphism.

In this talk we give some clarifying remarks describing the place of $\Theta ^0$ and $Aut(\Theta ^0)$ in the general set up of the universal algebraic geometry. Then we present the method of verbal operations which provides a machinery to calculate the group $St(\Theta^{0})$ and discuss some new results concerning the group of strongly stable automorphisms for the variety of non-associative algebras with unit.

          欢迎老师、同学们参加、交流！