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Article
Identities relating the Jordan product and the associator in the free nonassociative algebra
Journal of Algebra and Its Applications
  • Murray R. Bremner, University of Saskatchewan
  • Irvin R. Hentzel, Iowa State University
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
1-1-2006
DOI
10.1142/S0219498806001594
Abstract
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.
Comments

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:10.1142/S0219498806001594. http://www.worldscientific.com/. Posted with permission.

Copyright Owner
World Scientific Publishing
Language
en
File Format
application/pdf
Citation Information
Murray 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/