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$C_n$-cofinite twisted modules for $C_2$-cofinite vertex operator algebras

Daniel Tan

Abstract

Given a vertex operator algebra $ V $ with a general automorphism $ g $ of $ V $, we introduce a notion of $ C_n $-cofiniteness for weak $ g $-twisted $ V $-modules. When $ V $ is $ C_2 $-cofinite and of CFT type, we show that all finitely-generated weak $ g $-twisted $ V $-modules are $ C_n $-cofinite for all $ n \in \mathbb{Z}_{>0} $.

$C_n$-cofinite twisted modules for $C_2$-cofinite vertex operator algebras

Abstract

Given a vertex operator algebra with a general automorphism of , we introduce a notion of -cofiniteness for weak -twisted -modules. When is -cofinite and of CFT type, we show that all finitely-generated weak -twisted -modules are -cofinite for all .

Paper Structure

This paper contains 5 sections, 11 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Notation
  3. Acknowledgments
  4. Weak $g$-twisted $V$-modules
  5. Cofiniteness properties

Key Result

Proposition 1.2

For all $u \in V$, we have where we use $(Y_W)_0(u,x) = \sum_{n \in \mathbb{C}} u(n,0) x^{-n-1}$ to denote the series of log-free terms in $Y_W$.

Theorems & Definitions (31)

  • Definition 1.1
  • Proposition 1.2
  • proof
  • Proposition 1.3
  • Remark 1.4
  • Remark 1.5
  • Lemma 1.6
  • proof
  • Definition 2.1
  • Remark 2.2
  • ...and 21 more