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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
Article

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.

Keywords

Central Charge Vertex Operator Vertex Operator Algebra Conformal Weight Vertex Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

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