Rationality, Regularity, and C_2-cofiniteness

TL;DR

This paper proves that for CFT vertex operator algebras, C_2-cofiniteness and rationality are equivalent to regularity, and explores properties of C_2-cofinite algebras and modules.

Contribution

It establishes the equivalence between C_2-cofiniteness, rationality, and regularity for CFT vertex operator algebras, and analyzes modules and specific algebra classes.

Findings

C_2-cofiniteness and rationality imply regularity in CFT vertex operator algebras

Irreducible weak modules are ordinary modules for C_2-cofinite algebras

V_L^+ are C_2-cofinite

Abstract

We demonstrate that, for CFT vertex operator algebras, C_2-cofiniteness and rationality is equivalent to regularity. In addition, we show that, for C_2-cofinite vertex operators algebras, irreducible weak modules are ordinary modules and C_2-cofinite, and V_L^+ are C_2-cofinite.