# Automorphisms of the category of free non-associative algebras with unit

`2023-05-10 10:30:00``2023-05-10 11:30:00``Automorphisms of the category of free non-associative algebras with unit``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 subgroup $Inn(\Theta^0)$ of inner automorphisms and the subgroup $St(\Theta^0)$ of strongly stable automorphisms. In this talk we would like to give some clarifying remarks describing the place of $\Theta$ 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.``Third floor seminar room and Zoom``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`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 subgroup $Inn(\Theta^0)$ of inner automorphisms and the subgroup $St(\Theta^0)$ of strongly stable automorphisms.

In this talk we would like to give some clarifying remarks describing the place of $\Theta$ 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.

Last Updated Date : 28/04/2023