A Taste of PI-Theory

Given an associative algebra A over a field F, a polynomial identity for A is a polynomial in non-commuting variables that vanishes under all evaluations in A. An algebra satisfying a nontrivial polynomial identity is called a PI-algebra.
In this talk, we introduce some of the main results in PI-theory and several numerical invariants associated with polynomial identities, with particular emphasis on the use of combinatorial methods and representation theory techniques.
Finally, we will present some recent developments in the context of algebras with trace.