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ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

On Representations of Bol Algebras

Ndoune N1* and Bouetou Bouetou T2

1Department of Mathematics, University of Sherbrooke, Sherbrooke, (Québec), J1K 2R1, Canada

2Department of Mathematics and Computer Science, Polytechnic National High School of Yaounde, and Dâ €™ Excellence Centre Africain technologies €™ Information and Communication (CETIC) the Abdus Salam International Centre for Theoretical Physics (ICTP), POBox: 8390 Yaounde, Cameroon, France

Corresponding Author:
Ndoune N
Department of Mathematics, University of Sherbrooke, Sherbrooke
(Québec), J1K 2R1, Canada
Tel: +18198217000
E-mail: [email protected]

Received date: December 02, 2015; Accepted date: December 13, 2015; Published date: December 15, 2015

Citation: Ndoune N, Bouetou TB (2015) On Representations of Bol Algebras. J Generalized Lie Theory Appl S2:005. doi: 10.4172/2469-9837.1000S2-005

Copyright: © 2015 Ndoune N, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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.

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