Group gradings on upper block triangular matrices

Abstract

It was proved by Valenti and Zaicev, in 2011, that if G is an abelian group and K is an algebraically closed field of characteristic zero, then any G-grading on the algebra of upper block triangular matrices over K is isomorphic to a tensor product $M_n(K)\otimes UT(n_1,n_2,\ldots ,n_d)$, where $UT(n_1,n_2,\ldots ,n_d)$ is endowed with an elementary grading and $M_n(K)$ is provided with a division grading. In this manuscript, we prove the validity of the same result for a non necessarily commutative group and over an adequate field (characteristic either zero or large enough), not necessarily algebraically closed.