Prof. Antonio Giambruno, da Università degli studi di Palermo.

- Horário: 13hs
- Dia: 24/03
- Local: sala  S306-1 Bloco A

Title: Polynomial identities and central polynomials for n x n matrices
Abstract:  Let $A$ be an algebra over a field $F$. A polynomial in noncommuting variables $f(x_1, \ldots, x_n)$ is a central polynomial
of A$if$f(a_1, \ldots, a_n)$lies in the center of$A$, for all$a_1, \ldots, a_n \in A$. In case it takes only the value$0$,$f$is called a polynomial identity of$A$, whereas if it takes some non-zero value is called a proper central polynomials. The purpose of this talk is to discuss both polynomial identities and proper central polynomials of finite dimensional algebras. I will also be focusing on$M_n(F)$the algebra of$n \times n$matrices over$F\$.