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Article
Special identities for Bol algebras
Linear Algebra and its Applications
  • Irvin Roy Hentzel, Iowa State University
  • Luiz A. Peresi, University of São Paulo
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
4-1-2012
DOI
10.1016/j.laa.2011.09.021
Abstract

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two.

Comments

This article is published as Hentzel, Irvin R., and Luiz A. Peresi. "Special identities for Bol algebras." Linear Algebra and its Applications 436, no. 7 (2012): 2315-2330. doi: 10.1016/j.laa.2011.09.021. Posted with permission.

Creative Commons License
Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International
Copyright Owner
Elsevier Inc.
Language
en
File Format
application/pdf
Citation Information
Irvin Roy Hentzel and Luiz A. Peresi. "Special identities for Bol algebras" Linear Algebra and its Applications Vol. 436 Iss. 7 (2012) p. 2315 - 2330
Available at: http://works.bepress.com/irvin-hentzel/4/