Identities for generalized Lie and Jordan products on totally associative triple systems
type: Item
instance of: scholarly article
title: Identities for generalized Lie and Jordan products on totally associative triple systems
zbMATH Open document ID: 0999.17044
published in: Journal of Algebra
publication date: 2002-12-01T00:00:00Z
review text: The authors determine the identities of degree \(\leq 9\) satisfied by the new ternary operations \(abc+bca+cab+acb+cba+bac\) (symmetric sum), \(abc+bca+cab-acb-cba-bac\) (alternating sum), and \(abc+bca+cab\) (cyclic sum) on every triple system satisfying the total associativity identities \((abc)de=a(bcd)e=ab(cde)\). The first two operations are ternary analogs of the Lie and Jordan products, and the identities they satisfy may be regarded as ternary version of the Jacobi and Jordan identities. The authors did computations on computer using arithmetic modulo 103. For this reason, it is theoretically possible that there exist more identities, but these new identities should have all the integral coefficients congruent to zero modulo 103.
reviewed by: Ivan Shestakov
Mathematics Subject Classification ID: 17C50
zbMATH DE Number: 1525279
zbMATH Keywords: identities, triple systems, ternary Lie product
author: Murray R. Bremner
author: Irvin Roy Hentzel
MaRDI profile type: Publication
OpenAlex ID: W2039680887
Wikidata QID: Q115395766
cites work: Identities for the ternary commutator
cites work: New ternary versions of Jordan algebras
cites work: Special jordan identities
DOI: 10.1006/JABR.2000.8372
description: scientific article; zbMATH DE number 1525279