Abstract
With any semisimple Lie algebra g we can associate an infinite-dimensional Lie algebra AC (g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp 2n are obtained by the Poisson-bracket realizations method and AC (g) for g = sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case where g = sp 2.
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