Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

4-1-2012

Journal or Book Title

Linear Algebra and its Applications

Volume

436

Issue

7

First Page

2315

Last Page

2330

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 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

Included in

Algebra Commons

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