Let V be an affine algebraic variety over a commutative ring K and let A be the K-algebra of regular (polynomial) functions on V.
The group of automorphisms of V, namely Aut(A), is, generally speaking, not linear. We will discuss the following two questions: which properties of linear groups extend to Aut(A), and which properties of finite-dimensional Lie algebras extend to the Lie algebra Der(A) of vector fields on V?
In particular, we will focus on analogues of classical theorems of Selberg, Burnside, and Schur for Aut(A) and an analogue of the Engel theorem for Der(A). In order to achive natural degree of generality and to include some interesting non-commutative cases we prove the theorems for PI-algebras.
This is a joint work with O. Bezushchak and A. Petravchuk from Kyiv University.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
