On Representations of Bol Algebras
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
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.
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.