Cliffold algebras, modular Virasoro vertex operator algebras and Z[1/2]-forms

TL;DR

This paper constructs and classifies modular vertex operator algebras over fields of finite characteristic using Z[1/2]-forms, focusing on Virasoro and framed VOAs, and establishes their rationality and module structures.

Contribution

It introduces Z[1/2]-forms for Virasoro and framed vertex operator algebras, enabling classification and rationality results over various fields.

Findings

Constructed Z[1/2]-forms for Virasoro VOA with central charge 1/2.

Classified irreducible modules for these modular VOAs.

Established rationality of modular framed vertex operator algebras.

Abstract

This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex operator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex operator algebra over any field F of finite characteristic different from 2. We determine the generators and classify the irreducible modules for this vertex operator algebra. (2) We investigate modular framed vertex operator algebras. In particular, the rationality of modular framed vertex operator algebras is established. For a modular code vertex operator algebra, the irreducible modules are constructed and classified. Moreover, a Z[1/2]-form for any framed vertex operator algebra over complex field C is constructed. As a result, one can obtain a modular framed vertex operator algebra from any framed vertex operator algebra over C.