Graduações em Álgebras Matriciais

Abstract

The central theme of this dissertation is the study the of the gradings of a group G in the algebras UTn(F) and UT(d1; : : : ; dm). Initially, in Chapter 2, assuming G a finite abelian group and F an algebraically closed field and of characteristic zero, we prove that any grading in UTn(F) is elementary (up to graded isomorphism). Still in Chapter 2, without making any assumption about the group G and the field F, we obtain the same conclusion. To prove this was necessary to use more subtle techniques in demonstration. In Chapter 3, again assuming G a finite abelian group and F an algebraically closed field of characteristic zero, we classify the gradings of the algebra UT(d1; : : : ; dm). We will see that there is a decomposition d1 = tp1; : : : ; dm = tpm such that UT(d1; :::; dm) is isomorphic, as graded algebra, to the tensor product Mt(F) UT(p1; : : : ; pm), where Mt(F) has a fine grading and UT(p1; : : : ; pm) has a elementary grading.