A new class of nonassociative algebras with involution
type: Item
instance of: scholarly article
title: A new class of nonassociative algebras with involution
zbMATH Open document ID: 1165.17002
author: Noriaki Kamiya
author: Daniel Mondoc
published in: Proceedings of the Japan Academy. Series A
publication date: 2008-11-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1209649655
review text: Given a unital nonassociative algebra with involution \(({\mathcal A}, -)\) and \(\delta=\pm 1\), the operator \(V_{x,y}^\delta\) is defined by \(V_{x,y}^\delta(z)=(x\bar y)z+\delta((z\bar y)x-(z\bar x)y)\) for any \(x,y,z\in{\mathcal A}\). Then \(({\mathcal A},-)\) is said to be a \(\delta\)-structurable algebra in case \[ [V_{u,v}^\delta, V_{x,y}^\delta]=V_{V_{u.v}^\delta(x),y}^\delta-V_{x,V_{v,u}^\delta(y)}^\delta \] for any \(u,v,x,y\in {\mathcal A}\). For \(\delta=1\) this is the definition of structurable algebras, while for \(\delta=-1\) a new class of algebras appear. The paper under review is devoted to study the first properties of these algebras and related anti-Lie triple systems and Lie superalgebras.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 5362013
zbMATH Keywords: \(\delta\)-structurable algebra
zbMATH Keywords: triple system
zbMATH Keywords: Lie superalgebra
MaRDI profile type: Publication
OpenAlex ID: W2093277071
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DOI: 10.3792/PJAA.84.68
description: scientific article; zbMATH DE number 5362013