Leibniz homology of dialgebras of matrices

A dialgebra D is a vector space with two associative operations (sic), proves satisfying three more relations. By setting [x, y] := x (sic) y - y proves x, any dialgebra gives rise to a Leibniz algebra. Here we compute the Leibniz homology of the dialgebra of matrices gI(D) with entries in a given dialgebra D. We show that HL(gI(D)) is isomorphic to the tensor module over HHS(D), which is a variation of the natural dialgebra homology HHY(D). (C) 1998 Elsevier Science B.V. All rights reserved.