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A Comparison of Leibniz and Cyclic Homologies

Jerry Lodder
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Abstract

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.

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Jerry Lodder. 2005-07-08. A Comparison of Leibniz and Cyclic Homologies. https://arxiv.org/abs/math/0507165

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