%0 Journal Article
%T On Simple Completely Reducible Binary-Lie Superalgebras over sl<sub>2</sub>(F)
%A Manuel Arenas
%J Advances in Pure Mathematics
%P 314-323
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.55030
%X <p style=\"text-align:justify;\">
	<span style=\"font-size:12px;font-family:Verdana;\">In this article</span><span style=\"font-size:12px;font-family:Verdana;\">,</span><span style=\"font-size:12px;font-family:Verdana;\"> we prove that if</span><span style=\"font-size:12px;font-family:Verdana;\"> B</span><span style=\"font-size:12px;font-family:Verdana;\"> is a simple binary-Lie superalgebra whose even part is
isomorphic to sl<sub>2</sub>(F) &nbsp;and whose odd part is a completely reducible
binary-Lie-module over the even part, then</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> </span><span style=\"font-size:12px;font-family:Verdana;\">B is a Lie superalgebra. We introduce also a binary-Lie
module over which is sl<sub>2</sub>(F) not completely reducible.</span> 
</p>
%K Binary-Lie
%K Super-Algebras
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=55791