Identities relating the Jordan product and the associator in the free nonassociative algebra

dc.contributor.author Bremner, Murray
dc.contributor.author Hentzel, Irvin
dc.contributor.author Hentzel, Irvin
dc.contributor.department Mathematics
dc.date 2018-02-18T23:45:14.000
dc.date.accessioned 2020-06-30T05:59:47Z
dc.date.available 2020-06-30T05:59:47Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 2006
dc.date.issued 2006-01-01
dc.description.abstract <p>We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a○b = ab + ba and the associator [a,b,c] = (ab)c - a(bc) in every nonassociative algebra. In addition to the commutative identity a○b = b○a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a variety of binary-ternary algebras which generalizes the variety of Jordan algebras in the same way that Akivis algebras generalize Lie algebras.</p>
dc.description.comments <p>The electronic version of this article is published as "Identities relating the Jordan product and the associator in the free nonassociative algebra," Journal of Algebra and its Applications 5, no. 01 (2006): 77-88. doi:<a href="http://dx.doi.org/10.1142/S0219498806001594" target="_blank">10.1142/S0219498806001594</a>. http://www.worldscientific.com/. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/132/
dc.identifier.articleid 1137
dc.identifier.contextkey 10897466
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/132
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54516
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/132/2006_Hentzel_IdentitiesRelating.pdf|||Fri Jan 14 19:47:03 UTC 2022
dc.source.uri 10.1142/S0219498806001594
dc.subject.disciplines Algebra
dc.subject.disciplines Mathematics
dc.subject.keywords Nonassociative algebra
dc.subject.keywords ternary operations
dc.subject.keywords polynomial identities
dc.subject.keywords computational algebra
dc.title Identities relating the Jordan product and the associator in the free nonassociative algebra
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 70506428-9d7c-4c43-bcfa-d89bbb2149e4
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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