Degree-inverting involutions on matrix algebras

Abstract

Let F be an algebraically closed field of characteristic zero, and G be a finite abelian group. If A = circle times(g is an element of G)A(g) is a G-graded algebra, we study degree-inverting involutions on A, i.e. involutions * on A satisfying (A(g))* subset of A(g-1), for all g is an element of G. We describe such involutions for the full nxn matrix