The second homology group of current Lie algebras

Details The second homology group of current Lie algebras The second homology group of current Lie algebras

2008-08-01

arxiv.org/abs/0808.0217v4

Ast\'erisque 226 (1994), 435-452

Mathematics

K-Theory and Homology

v4: fixed few typos and confusing notation

Scientific paper

This is an old paper put here for archeological purposes. We derive a general formula expressing the second homology of a Lie algebra of the form L\otimes A with coefficients in the trivial module through homology of $L$, cyclic homology of $A$, and other invariants of $L$ and $A$. This is achieved by using the Hopf formula expressing the second homology of a Lie algebra in terms of its presentation. We also derive a similar formula for the associated Lie algebra of the tensor product of two associative algebras.

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