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Advances in Mathematical Physics
Volume 2013, Article ID 938901, 7 pages
Research Article

Representations of 3-Dimensional Simple Multiplicative Hom-Lie Algebras

Department of Mathematics, Tongji University, Shanghai 200092, China

Received 6 July 2013; Accepted 23 September 2013

Academic Editor: Wen-Xiu Ma

Copyright © 2013 Xiuxian Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to study representations of 3-dimensional simple multiplicative Hom-Lie algebras (whose structure is of A1-type). In this paper we can see that a finite dimensional representation of is not always completely reducible, and a representation of is irreducible if and only if it is a regular Lie-type representation.