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Semi-infinite cohomology and superconformal algebras

Elena Poletaeva
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Abstract

We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a non-degenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, which is analogous to the classical structure of the de Rham cohomology in Kähler geometry.

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Elena Poletaeva. 2000-12-20. Semi-infinite cohomology and superconformal algebras. https://arxiv.org/abs/math/0012195

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