Omni-Representations of Leibniz Algebras

Abstract

In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra g on a vector space V as a Leibniz algebra homomorphism from g to the omni-Lie algebra gl(V)⊕V. Then we introduce the omnicohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.