V-Algebras and Their Free Field Realizations

Details V-Algebras and Their Free Field Realizations V-Algebras and Their Free Field Realizations

1997-03-20

arxiv.org/abs/hep-th/9703140v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex, no figures

Scientific paper

The V-algebras are the non-local matrix generalization of the well-known W-algebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the general Miura transformation, we give the decomposition theorems for the second Poisson brackets, from which we are able to construct the free field realizations for a class of V-algebras including V_{(2k,2)}-algebras that corresponds to the Lie algebra of C_k-type as the particular examples. The reduction of our discussion to the scalar case provides the similar result for the W_{BKP}-algebra.

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