Gradings induced by nilpotent elements
type: Item
instance of: scholarly article
title: Gradings induced by nilpotent elements
author: E. Garcia
author: Rubén Muñoz Alcázar
author: Guillermo Vera de Salas
author: Miguel Gómez Lozano
published in: Linear Algebra and its Applications
publication date: 2022-11-08T00:00:00Z
review text: In this paper the authors prove that any nilpotent last-regular element \(a\) in an associative algebra \(R\) over a ring of scalars \(\Phi\) gives rise to a complete system of orthogonal idempotents that induces a finite \(\mathbb{Z}\)-grading on \(R\); Further, they show that such element gives rise to an \(\mathfrak{sl_2}\)-triple in \(R\) with semisimple adjoint map \(ad_h\), and that the grading of \(R\) with respect to the complete system of orthogonal idempotents is a refinement of the \(\Phi\)-grading induced by the eigenspaces of \(ad_h\).
reviewed by: R. Udhayakumar
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 7613287
zbMATH Keywords: von Neumann regular
zbMATH Keywords: nilpotent element
zbMATH Keywords: grading
zbMATH Keywords: \( \mathfrak{sl}_2\)-triple
MaRDI profile type: Publication
full work available at URL: j.laa.2022.09.017
OpenAlex ID: W4296676400
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DOI: 10.1016/J.LAA.2022.09.017
description: scientific article; zbMATH DE number 7613287