G-graduações das álgebras de matrizes triangulares superiores sobre um corpo

Abstract

Let F be a field and G a group. In this dissertation, we deal with the G-gradings of the algebra of upper triangular matrices over F, based on Valenti and Zaicev's articles on the subject. We start by the 2x2 matrices case, which shows in a simpler manner the techniques used on the more general cases. We then deal with the case where n is arbitrary, but first will restrict ourselves to the case F is an algebraically closed field of characteristc zero and G an finite abelian group. Lastly, we will do thegeneral case: If F is any field and G any group, then every G-grading of the algebra of upper triangular matrices over F is isomorphic to a kind we call elementary.