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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier Inc.
Copyright Date
2011
Language
en
File Format
application/pdf
Recommended Citation
Hentzel, Irvin Roy and Peresi, Luiz A., "Special identities for Bol algebras" (2012). Mathematics Publications. 127.
https://lib.dr.iastate.edu/math_pubs/127
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.