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The Cohomology Algebra of the Semi-Infinite Weil Complex

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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 \(\mathbb{Z}\)-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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Authors and Affiliations

  1. Department of Mathematics, Brandeis University, Waltham, MA, 02454, USA

    Andrew R. Linshaw

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  1. Andrew R. Linshaw
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Correspondence to Andrew R. Linshaw.

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Communicated by L. Takhtajan

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Linshaw, A.R. The Cohomology Algebra of the Semi-Infinite Weil Complex. Commun. Math. Phys. 267, 13–23 (2006). https://doi.org/10.1007/s00220-006-0062-9

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  • DOI: https://doi.org/10.1007/s00220-006-0062-9

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