Abstract
ABSTRACTWe construct and study the map from Leibniz homology HL∗(𝔥) of an abelian extension 𝔥 of a simple real Lie algebra 𝔤 to the Hochschild homology HH∗−1(U(𝔥)) of the universal envelopping algebra U(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.
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