Dedekind's η-function and the cohomology of infinite dimensional Lie algebras
- 1 July 1975
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 72 (7) , 2493-2495
- https://doi.org/10.1073/pnas.72.7.2493
Abstract
We compute the cohomology of certain infinite dimensional Lie algebras which are subalgebras of Lie algebras introduced by Moody and Kac. We note a relation between our results and the cohomology of loop spaces of compact groups. Finally, we derive, by Euler-Poincaré, identities of Macdonald for powers of the Dedekind eta-function.Keywords
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