Cohomology of Leibniz triple systems with derivations

Abstract

In this paper, we introduce the notion of a LeibtsDer pair, i.e., a Leibniz triple system with a derivation. We define a representation of a LeibtsDer pair and the corresponding cohomology theory. We prove that a LeibtsDer pair is rigid if the HD3(L,L)=0, and a deformation of order n is extensible if its obstruction class (Ob(μt,Dt)i3,Ob(μt,Dt)1)=∂i3(μn+1,Dn+1)(i=1,2). We also show that the central extensions of a LeibtsDer pair can be classified by the third cohomology group.