Conference abstracts

Session S05 - Rings and Algebras

No date set

## Involution inverting gradings on matrix algebras

### Universidade Federal de São Paulo, Brasil   -   castilho.thiago@gmail.com

Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $M_n(F)$ is an algebra with involution $*$, we describe $G$-gradings $M_n(F)=A=\oplus_{g\in G} A_g$ on $A$, satisfying $(A_g)^*\subseteq A_{g^{-1}}$, for all $g\in G$.

Joint work with Luís Felipe Gonçalves Fonseca (Universidade Federal de Viçosa).