# Group gradings on upper block triangular matrices

Authors
• 1 Universidade Estadual de Campinas, Campinas, SP, 13083-859, Brazil , Campinas (Brazil)
• 2 Memorial University of Newfoundland, Department of Mathematics and Statistics, St. John’s, NL, A1C5S7, Canada , St. John’s (Canada)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Springer International Publishing
Publication Date
Jan 05, 2018
Volume
110
Issue
4
Pages
327–332
Identifiers
DOI: 10.1007/s00013-017-1134-0
Source
Springer Nature
Keywords
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 Mn(K)⊗UT(n1,n2,…,nd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_n(K)\otimes UT(n_1,n_2,\ldots ,n_d)$$\end{document}, where UT(n1,n2,…,nd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$UT(n_1,n_2,\ldots ,n_d)$$\end{document} is endowed with an elementary grading and Mn(K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_n(K)$$\end{document} 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.