Seminario Teoría de grupos

14/02

11:30 Aula Naranja ICMAT

Speaker: Ofir Schnabel (Ort Braude College)

Title: Group-graded algebras and the intrinsic fundamental group

Abstract: The intrinsic fundamental group of an algebra A is essentially the inverse limit of a diagram whose objects are groups which grade A in a connected way, and whose morphisms are group epimorphisms which correspond to quotient morphisms between these gradings. The computation of the intrinsic fundamental group consist of three steps:

1. Classify all the connected gradings of A up to equivalence of gradings.

2. Compute the quotient grading morphisms between the above grading classes.

These two steps yield a diagram of groups and homomorphisms.

3. To calculate the inverse limit of this diagram.

This is often the hardest of the above three challenges.

In this talk, we will focus on the intrinsic fundamental group of finite dimensional semisimple complex algebras and in particular matrix algebras and diagonal algebras. In these cases, the above diagram is always finite and the intrinsic fundamental group is its pullback.