Leibniz homilogy of dialgebras of matrices Original Research Article

A dialgebra D is a vector space with two associative operations ÷, vertical, dash satisfying three more relations. By setting [x, y] : = x ÷ y − y vertical, dash x, any dialgebra gives rise to a Leibniz algebra. Here we compute the Leibniz homology of the dialgebra of matrices gl(D) with entries in a given dialgebra D. We show that HL(gl(D)) is isomorphic to the tensor module over HHS(D), which is a variation of the natural dialgebra homology HHY(D).