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C2C_2-cofiniteness of finite-group orbifolds

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebra

Contributed by Andrew Riesen ↗

Version 1 / Oct 29, 2026 / CC BY 4.0

Abstract

Let VV be a simple vertex algebra with a connected nonnegative integer grading, and let GG be a finite group of grading-preserving automorphisms. We prove that C2C_2-cofiniteness of VV implies C2C_2-cofiniteness of VGV^G. The proof bounds the length and height of monomials in strong generators representing classes in a relative C2C_2 quotient. The length bound follows from a good filtration and finite-group invariant theory. The height bound follows from differential equations for products of fields, together with identities for invariants and vacuum coefficients. The height bound also shows that finite strong generation passes to VGV^G, without assuming C2C_2-cofiniteness. For strongly rational vertex operator algebras, the cofiniteness result and McRae's orbifold theorem imply strong rationality of every finite-group fixed-point algebra.

Provenance statement

Initial manuscript, with further expositional refinements and clarifications forthcoming. The author understands the overall argument and has verified many of its details. A small number of technical points remain under detailed review, which is expected to be completed in the coming days.

References

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Version history

  1. v1Submitted by Andrew RiesenInitial depositCurrentOct 29, 2026