Conference abstracts

Session S05 - Rings and Algebras

July 28, 15:45 ~ 16:10

## Polynomial identities, codimensions and a conjecture of Regev

### Antonio Giambruno

### Università di Palermo, Italy - antonio.giambruno@unipa.it

Let $A$ be an algebra over a field $F$ of characteristic zero and $Id(A)$ its T-ideal of identities. The space of multilinear polynomials in $n$ fixed variables modulo $Id(A)$ is a representation of the symmetric group $S_n$ and its degree is called the $n$th codimension of $A$. As soon as $A$ is associative and satisfies a non-trivial identity, its sequence of codimensions is exponentially bounded and, following a conjecture of Amitsur regarding its exponential growth, Regev made a conjecture about the precise asymptotics of such sequence. I will talk about the results around this conjecture also in the case of non associative algebras.