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arXiv · 1901.08869

Group gradings on upper block triangular matrices

Felipe Yukihide Yasumura
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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 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.

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Felipe Yukihide Yasumura. 2019-01-25. Group gradings on upper block triangular matrices. https://doi.org/10.1007/s00013-017-1134-0

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