Communications in Mathematical Physics

, Volume 267, Issue 1, pp 13–23 | Cite as

The Cohomology Algebra of the Semi-Infinite Weil Complex

  • Andrew R. LinshawEmail author


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.


Central Charge Vertex Operator Vertex Operator Algebra Conformal Weight Vertex Algebra 
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© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

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