Cliffold algebras, modular Virasoro vertex operator algebras and Z[1/2]-forms
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.
Keywords
Cite
@article{arxiv.1709.04167,
title = {Cliffold algebras, modular Virasoro vertex operator algebras and Z[1/2]-forms},
author = {Chongying Dong and Ching Hung Lam and Li Ren},
journal= {arXiv preprint arXiv:1709.04167},
year = {2021}
}
Comments
41 pages. The new version has changed significantly. We add the following new results: 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