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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 354341, 11 pages
http://dx.doi.org/10.1155/2015/354341
Research Article

Structures and Low Dimensional Classifications of Hom-Poisson Superalgebras

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China

Received 4 May 2015; Accepted 4 August 2015

Academic Editor: Hoshang Heydari

Copyright © 2015 Qingcheng Zhang et al. 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.

Abstract

Hom-Poisson superalgebras can be considered as a deformation of Poisson superalgebras. We prove that Hom-Poisson superalgebras are closed under tensor products. Moreover, we show that Hom-Poisson superalgebras can be described using only the twisting map and one binary operation. Finally, all algebra endomorphisms on 2-dimensional complex Poisson superalgebras are computed, and their associated Hom-Poisson superalgebras are described explicitly.