A Hilbert theorem for vertex algebras

Abstract

Given a simple vertex algebra A and a reductive group G of automorphisms of A, the invariant subalgebra A^G is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally not true of the classical limit of A^G, which often requires infinitely many generators and infinitely many relations to describe. Using tools from classical invariant theory, together with recent results on the structure of the W_{1+\infty} algebra, we establish the strong finite generation of a large family of invariant subalgebras of βγ-systems, bc-systems, and bcβγ-systems.

A few typos corrected, final version

Cited by in corpus (12)

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• Cosets of affine vertex algebras inside larger structures
• Simple current extensions beyond semi-simplicity
• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
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• The structure of the Kac-Wang-Yan algebra
• Invariant subalgebras of affine vertex algebras
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• Arc spaces and the vertex algebra commutant problem
• $N=4$ superconformal algebras and diagonal cosets
• Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$
• Finiteness and orbifold Vertex Operator Algebras