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 $M_n(K)\otimes UT(n_1,n_2,\dots ,n_d)$, where $UT(n_1,n_2,\dots ,n_d)$ is endowed with an elementary grading and $M_n(K)$ is provided with a division grading. In this paper, 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.

More details were included in the proof of the main result

Cited by in corpus (2)

• Group gradings on the Lie and Jordan algebras of block-triangular matrices
• Homogeneous involutions on upper triangular matrices