Upper triangular, and more generally, block-triangular matrices, are rather important in linear algebra, and also in ring theory, namely in the theory of PI algebras. The group gradings on such algebras have been studied extensively during the last decades. In 2007 A. Valenti and M. Zaicev conjectured that every grading on these algebras is obtained from an elementary grading on a block-triangular matrix algebra and a division grading on a matrix algebra. In this talk we present recent results on this problem.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
