Year: 2026
Type: preprint
Abstract: The notion of admissible $g$-twisted $V$-comodules is investigated for a graded vertex operator coalgebra $V$ and a finite order automorphism $g\in \Aut V$. We prove that $\mathcal {M}$ is an admissible $g$-twisted $V$-comodule if and only if its graded dual $\mathcal {M}'$ is an admissible $g^{-1}$-twisted $V'$-module for vertex operator algebra $V'$. Then we establish a dual theory of twisted Zhu's theory, i.e., there is a coassociative coalgebra $C_g(V)$ for a graded vertex operator coalgebra $V$, any admissible $g$-twisted $V$-comodule gives a $C_g(V)$-comodule, and vice versa. We also prove that $V$ is $g$-corational, which means every admissible $g$-twisted $V$-comodule is completely reducible, if and only if its dual vertex operator algebra $V'$ is $g$-rational.
Source: arXiv (Cornell University)
Author: Wang, Hao
Institution: Northwest University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G254172227
OpenAlex ID: W7212081285