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arXiv · 0808.0217

The second homology group of current Lie algebras

Pasha Zusmanovich
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Abstract

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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Pasha Zusmanovich. 2008-08-01. The second homology group of current Lie algebras. https://arxiv.org/abs/0808.0217

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