Minimal superalgebras generating minimal supervarieties
type: Item
instance of: scholarly article
title: Minimal superalgebras generating minimal supervarieties
zbMATH Open document ID: 1454.16030
author: Viviane Ribeiro Tomaz da Silva
author: Ernesto Spinelli
author: M. Onofrio Di Vincenzo
published in: Mathematische Zeitschrift
publication date: 2018-03-21T00:00:00Z
review text: In characteristic zero the generators of the minimal supervarieties of finite basic rank belong to the class of \textit{minimal superalgebras} introduced in [\textit{A. Giambruno} and \textit{M. Zaicev}, Trans. Am. Math. Soc. 355, No. 12, 5091--5117 (2003; Zbl 1031.16015)]. The authors give a complete list of minimal supervarieties generated by minimal superalgebras whose maximal semisimple homogeneous subalgebra is the sum of three graded simple algebras. As a consequence, they give a negative answer to the question of whether any minimal superalgebra generates a minimal supervariety.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16W55
zbMATH DE Number: 6851632
zbMATH Keywords: superalgebras
zbMATH Keywords: graded polynomial identities
zbMATH Keywords: superexponent
zbMATH Keywords: minimal supervarieties
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
full work available at URL: s00209-017-1893-0
OpenAlex ID: W2614957944
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DOI: 10.1007/S00209-017-1893-0
description: scientific article; zbMATH DE number 6851632