On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras
type: Item
instance of: scholarly article
title: On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras
zbMATH Open document ID: 0998.16024
published in: Journal of Algebra
publication date: 2002-08-25T00:00:00Z
review text: An algebra \(D\) is called third power associative in case \((xx)x=x(xx)\) for all \(x\in D\). The authors describe third power associative multiplications \(*\) on noncentral Lie ideals of prime associative algebras and skew elements of prime algebras with involution provided that \(x*y-y*x=[x,y]\) for all \(x,y\) and the prime algebras in question do not satisfy polynomial identities of low degree. The authors also obtain necessary and sufficient conditions for these multiplications to be fourth power associative or flexible.
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 17D25
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 16R50
zbMATH DE Number: 1556975
zbMATH Keywords: Lie-admissible algebras
zbMATH Keywords: Jordan-admissible algebras
zbMATH Keywords: prime algebras
zbMATH Keywords: Lie-compatible multiplications
zbMATH Keywords: Jordan-compatible multiplications
zbMATH Keywords: third power associative algebras
zbMATH Keywords: polynomial identities
zbMATH Keywords: Lie ideals
zbMATH Keywords: skew elements
zbMATH Keywords: algebras with involutions
Wikidata QID: Q115395760
author: K. I. Beidar
author: M. A. Chebotar
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
full work available at URL: jabr.2000.8449
OpenAlex ID: W2085154099
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DOI: 10.1006/JABR.2000.8449
description: scientific article; zbMATH DE number 1556975