arXiv subjects

Chongying Dong

Publications and source records attributed to Chongying Dong.

93 records · Page 6Linked to original sources

arXiv1994

On the operator content of nilpotent orbifold models

Let $V$ be a simple vertex operator algebra and $G$ be a finite nilpotent group of automorphisms of $V.$ We prove the following in this paper: (1) There is a Galois correspondence between subgroups of $G$ and the vertex operator subalgebras of $V$ which contain $V^G$ given by the map $H\mapsto V^H.$ (2) Assume that for every G\in G$ there is unique simple $g$-twisted $V$-module $M(g).$ Then there exists a Hochschild 3-cocycle $α$ on the integral group $Z[G]$ such that there is an equivalence of categories between $V^G$-module category (whose objects are $V^G$-submodules of direct sums of copies of $\oplus_{g\in G}M(g),$ and whose morphisms are $V^G$-module homomorphisms) and the module category for the twisted quantum double $D_α(G)$ associated to $α.$

hep-th↗

arXiv1994

On quantum Galois theory

For a simple vertex operator algebra $V$ and a finite automorphism group $G$ of $V$ then $V$ is a direct sum of $V^χ$ where $χ$ are irreducible character of $G$ and $V^χ$ is the subspace of $V$ which $G$ acts according to the character $χ.$ We prove the following: 1. Each $V^χ$ is nonzero. 2. $V^χ$ is a tensor product $M_χ\otimes V_χ$ where $M_χ$ is an irreducible $G$-module affording $χ$ and $V_χ$ is a $V^G$-module. If $G$ is solvable, $V_χ$ is a simple $V^G$-module and $M_χ\mapsto $V_χ$ is a bijection from the set of irreducible $G$-modules to the set of (inequivalent) simple $V^G$-modules which are contained in $V.$

hep-th↗

arXiv1994

Induced modules for vertex operator algebras

For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a $g$-twisted induction functor from the category of $g$-twisted $V'$-modules to the category of $g$-twisted $V$-modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated with $V$ being simple or with $V'$ being $g$-rational.

hep-th↗