A Comparison of Leibniz and Cyclic Homologies

We relate Leibniz homology to cyclic homology by studying a map from a long exact sequence in the Leibniz theory to the ISB periodicity sequence in the cyclic theory. This provides a setting by which the two theories can be compared via the 5-lemma. We then show that the Godbillon-Vey invariant, as detected by the Leibniz homology of formal vector fields, maps to the Godbillon-Vey invariant as detected by the cyclic homology of the universal enveloping algebra of these vector fields.