Invariant subalgebras of affine vertex algebras

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.

Final version, proof of main result simplified. arXiv admin note: substantial text overlap with arXiv:1006.5620

References in corpus (3)

• Invariant theory and the Heisenberg vertex algebra
• A Hilbert theorem for vertex algebras
• Invariant theory and the W_{1+\infty} algebra with negative integral central charge

Cited by in corpus (13)

• Schur-Weyl Duality for Heisenberg Cosets
• Cosets of affine vertex algebras inside larger structures
• Simple current extensions beyond semi-simplicity
• Trialities of $\mathcal{W}$-algebras
• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
• Invariant theory and the Heisenberg vertex algebra
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• $N=4$ superconformal algebras and diagonal cosets
• Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$
• Generalized parafermions of orthogonal type
• The ${\mathbb{Z}}_2$-orbifold of the ${\mathcal{W}}_3$-algebra
• On the structure of W-algebras in type A
• Orbifolds of Gaiotto-Rapčák $Y$-algebras