A way to measure a T-ideal of the free associative algebra in characteristic zero is through the sequence of codimensions introduced by Regev in 1972. It is known that for any non-trivial T-ideal such sequence either grows exponentially or is polynomially bounded. We shall describe what kind of functions arise and how they can determine some invariants of the T-ideals that can be explicitly computed in some cases.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
