Invariant subalgebras of affine vertex algebras

Details Invariant subalgebras of affine vertex algebras Invariant subalgebras of affine vertex algebras

2010-11-10

arxiv.org/abs/1011.2281v3

Mathematics

Quantum Algebra

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Scientific paper

Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of automorphisms of V_k(g,B), we show that the invariant subalgebra V_k(g,B)^G is strongly finitely generated for generic values of k. This implies the existence of a new family of deformable W-algebras W(g,B,G)_k which exist for all but finitely many values of the parameter k.

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