Central exponent in PI-theory

Abstract: The algebras that satisfy at least a non-trivial polynomial identity are called PI-algebras. They can be seen as a generalization of the commutative world and PI-theory is the research field in modern algebra studying the identities satisfied by these algebras. In its general case this is a very difficult problem, so that a combinatoric approach is generally used.

We will briefly introduce polynomial identities and PI-algebras, giving also some motivations, and we will present the main results in PI-theory.

Then, we will introduce central polynomials, explaining why they are important for the research on polynomial indentities. Their behavior can be also studied by analyzing the behavior of the dimension $c_n^z(A)$ of the space of multilinear polynomials of degree $n$ modulo the central polynomials of an associative PI-algebra $A$. In 2018, Giambruno and Zaicev established, for associative algebras, the existence of the limit $$ \lim_{n \to \infty} \sqrt[n]{c_n^z(A)}. $$ In this talk we present research advances on this problem, with special focus on associative superalgebras with superinvolution.

This talk is based on a joint work with Antonio Ioppolo, Antônio Augusto dos Santos and Ana Cristina Vieira.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar