The Cohomology Algebra of the Semi-infinite Weil Complex

Details The Cohomology Algebra of the Semi-infinite Weil Complex The Cohomology Algebra of the Semi-infinite Weil Complex

2005-01-09

arxiv.org/abs/math/0501117v3

Commun. Math. Phys. 267, 13-23 (2006).

Mathematics

Quantum Algebra

Minor editorial changes, references added

Scientific paper

10.1007/s00220-006-0062-9

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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