Semiinfinite Weil complex and the Virasoro algebra
Abstract
We define a semiinfinite analogue of the Weil algebra associated an infinitedimensional Lie algebra. It can be used for the definition of semiinfinite characteristic classes by analogy with the ChernWeil construction. The second term of a spectral sequence of this Weil complex consists of the semiinfinite cohomology of the Lie algebra with coefficients in its "adjoint semiinfinite symmetric powers." We compute this cohomology for the Virasoro algebra. This is just the BRST cohomology of the bosonic βγsystem with central charge 26. We give a complete description of the Fock representations of this bosonic system as modules over the virasoro algebra, using FriedanMartinecShenker bosonization. We derive a combinatorial identity from this result.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 April 1991
 DOI:
 10.1007/BF02100281
 Bibcode:
 1991CMaPh.137..617F
 Keywords:

 Neural Network;
 Statistical Physic;
 Complex System;
 Nonlinear Dynamics;
 Central Charge