Idempotents and Peirce gradings of Jordan algebras
type: Item
instance of: scholarly article
title: Idempotents and Peirce gradings of Jordan algebras
zbMATH Open document ID: 1155.17012
author: Teresa Cortés
author: José A. Anquela
published in: Journal of Algebra
publication date: 2008-12-05T00:00:00Z
review text: The authors give a necessary condition on Peirce gradings of a Jordan algebra \(J\) for them to come from idempotents in a bigger algebra. The natural extension of \(J\) where the idempotent element should be found is constructed. It is proved that this necessary condition is also sufficient for Jordan algebras without 2-torsion, and it holds automatically in sufficiently regular (for example, nondegenerate) Jordan algebras. Also the authors consider Peirce gradings of associative algebras and show that they always come from idempotents in bigger algebras. The authors prove that not all Peirce gradings in special Jordan algebras are induced by associative Peirce gradings.
Mathematics Subject Classification ID: 17C27
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 5378358
zbMATH Keywords: idempotent
zbMATH Keywords: Jordan algebra
zbMATH Keywords: Peirce grading
reviewed by: Alexandre P. Pojidaev
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.07.022
OpenAlex ID: W1976823046
cites work: Peirce gradings of Jordan systems
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DOI: 10.1016/J.JALGEBRA.2008.07.022
description: scientific article; zbMATH DE number 5378358