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The Cohomology Algebra of the Semi-infinite Weil Complex

Andrew R. Linshaw
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Abstract

In 1993, Lian-Zuckerman constructed two cohomology operations on the BRST complex of a conformal vertex algebra with central charge 26. They gave explicit generators and relations for the cohomology algebra equipped with these operations in the case of the c=1 model. In this paper, we describe another such example, namely, the semi-infinite Weil complex of the Virasoro algebra. The semi-infinite Weil complex of a tame Z-graded Lie algebra was defined in 1991 by Feigin-Frenkel, and they computed the linear structure of its cohomology in the case of the Virasoro algebra. We build on this result by giving an explicit generator for each non-zero cohomology class, and describing all algebraic relations in the sense of Lian-Zuckerman, among these generators.

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Andrew R. Linshaw. 2006-04-18. The Cohomology Algebra of the Semi-infinite Weil Complex. https://doi.org/10.1007/s00220-006-0062-9

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