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arXiv · 1011.2281

Invariant subalgebras of affine vertex algebras

Andrew R. Linshaw
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Abstract

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 k.

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BibTeXRIS

Andrew R. Linshaw. 2010-11-10. Invariant subalgebras of affine vertex algebras. https://doi.org/10.1016/j.aim.2012.10.015

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