Kiinneth-style formula for the homology of Leibniz algebras

There is another type of homology theory for Lie algebras : the Leibniz homology HL,(I~), defined as the homology of a complex (T g, d) where T ~ is the tensor module over g and the differential is a lifting of the preceding differential. In fact this theory is defined for a larger class of algebras : the Leibniz algebras (see 1 below). The aim of this paper is to compute HL.(I~ @gl) in terms of HL.(~) and HL.(g~). The result is as follows. For any Leibniz algebras O and g' over the field k, there is a canonical isomorphism of graded vector spaces