Leibniz and Hochschild homology.

We construct and study the map from Leibniz homologyHL∗(𝔥) of an abelian extension𝔥of a simple real Lie algebra𝔤to the Hochschild homologyHH∗−1(U(𝔥)) of the universal envelopping algebraU(𝔥). To calculate some homology groups, we use the Hochschild-Serre spectral sequences and Pirashvili spectral sequences. The result shows what part of the non-commutative Leibniz theory is detected by classical Hochschild homology, which is of interest today in string theory. [ABSTRACT FROM PUBLISHER]