Ualbai Umirbaev: Automorphism groups of free algebras

4th December, 2020
Watch Later Cinema Mode

There are many interesting results on the structure of the automorphism group Aut(Fn) and the outer automorphism group Out(Fn) of the free group Fn of rank n. Unfortunately, the theory of automorphism groups of free algebras over a field is not very rich and many problems are still open. I will describe some results and recall some open questions on the structures of the automorphism groups of:

  1. the polynomial algebra K[x1,x2,…,xn] of rank n over a field K;
  2. the free associative algebra K<x1,x2,…,xn> of rank n over K; and
  3. the free Lie algebra Lie<x1,x2,…,xn> of rank n over K.

This video is part of the New York Group Theory Cooperative‘s Manhatten algebra day.