On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
A. A. Balinsky, A. I. Balinsky
Abstract
The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions with the problem of quntization of hydrodynamics brackets is demonstrated.
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