Journal of Generalized Lie Theory and Applications

On Representations of Bol Algebras

N Ndoune and T Bouetou Bouetou

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Abstract

In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical Engel’s theorem and the extension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations of Bol algebras and show that it is a tensor category. In the case of regular representations of Bol algebras, we give a complete classification of them for all two-dimensional Bol algebras.

Article information

Source
J. Gen. Lie Theory Appl., Volume 10, Number S2 (2016), 6 pages.

Dates
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1479265224

Digital Object Identifier
doi:10.4172/1736-4337.1000S2-005

Mathematical Reviews number (MathSciNet)
MR3663974

Zentralblatt MATH identifier
06673123

Keywords
Bol algebra Lie triple System Non-associative algebras Jordan superalgebras Nilpotent representation

Citation

Ndoune, N; Bouetou Bouetou, T. On Representations of Bol Algebras. J. Gen. Lie Theory Appl. 10 (2016), no. S2, 6 pages. doi:10.4172/1736-4337.1000S2-005. https://projecteuclid.org/euclid.jglta/1479265224


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