Some Leibniz bimodules of ${\mathfrak{sl}}_2$

Abstract

We study complex finite-dimensional Leibniz algebra bimodule over ${\mathfrak{sl}}_2$ that as a Lie algebra module is split into a direct sum of two simple ${\mathfrak{sl}}_2$-modules. We prove that in this case there are only two non-split Leibniz ${\mathfrak{sl}}_2$-bimodules and we describe the actions.

arXiv admin note: text overlap with arXiv:1111.4631 by other authors