Categorification of Virasoro-Magri Poisson vertex algebra
Abstract
Let S be the direct sum of algebra of symmetric groups C Sn for a non-negative integer n. We show that the Grothendieck group K0(S) of the category of finite dimensional modules of S is isomorphic to the differential algebra of polynomials Z[Dn x]. Moreover, for a non-negative integer m, we define m-th products on K0(S) which make the algebra K0(S) isomorphic to an integral form of the Virasoro-Magri Poisson vertex algebra. Also, we investigate relations between K0(S) and K0(N) where K0(N) is the direct sum of Grothendieck groups K0(Nn) of finitely generated projective Nn-modules. Here Nn is the nil-Coxeter algebra generated by n-1 elements.
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