A Hilbert theorem for vertex algebras

2009/03/31 by Andrew R. Linshaw · 16 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Automorphism #Automorphism group #Direct limit #Finitely-generated abelian group #Hilbert–Poincaré series #Invariant (physics) #Invariant theory #Subalgebra #Vertex (graph theory) #math.QA #math.RT

paper · pdf · doi:10.1007/s00031-010-9087-4

published in Transformation Groups 15(2), 427-448 (Birkhäuser) · A few typos corrected, final version

openalex publication_date 2010/04/08 · arxiv created 2010/11/10 · openalex created_date 2016/06/24 · arxiv updated 2020/08/10 · openalex updated_date 2026/08/05

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+∞ algebra, we establish the strong finite generation of a large family of invariant subalgebras of βγ-systems, bc-systems, and bcβγ-systems.

Citations

• Invariant chiral differential operators and the W3 algebra
• Local systems of vertex operators, vertex superalgebras and modules
• Vertex algebras, Kac-Moody algebras, and the Monster

Cited by

• The Structure of the Kac–Wang–Yan Algebra