Identities relating the Jordan product and the associator in the free nonassociative algebraJournal of Algebra and Its Applications
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AbstractWe 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.
Copyright OwnerWorld Scientific Publishing
Citation InformationMurray R. Bremner and Irvin R. Hentzel. "Identities relating the Jordan product and the associator in the free nonassociative algebra" Journal of Algebra and Its Applications Vol. 5 Iss. 1 (2006) p. 77 - 88
Available at: http://works.bepress.com/irvin-hentzel/17/