Generalized twisted modules associated to general automorphisms of a vertex operator algebra
type: Item
instance of: scholarly article
title: Generalized twisted modules associated to general automorphisms of a vertex operator algebra
zbMATH Open document ID: 1233.17025
author: Yi-Zhi Huang
published in: Communications in Mathematical Physics
publication date: 2010-08-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/0905.0514
review text: Twisted modules play an important crucial role in the orbifold theory of vertex operator algebras. In the paper under review, the author introduces a notion of generalized \(g\)-twisted modules, where \(g\) is not necessarily finite. When \({V=\coprod_{n\in \mathbb{Z}}V_{(n)}}\) is a vertex operator algebra such that \({V_{(0)}=\mathbb{C}\mathbf{1}}\) and \(V _{(n)} = 0\) for \(n < 0\) and \(g =\exp{({2\pi \sqrt{-1}\; {\text{Res}}_{x} Y(u, x)})}\), where \(u\) is an element of \(V\) of weight 1 such that \(L(1)u = 0\), a construction of such twisted modules is given using some \(\Delta\)-operator. In particular, examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet \(W\)-algebras are given.
reviewed by: Ching Hung Lam
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 5764631
zbMATH Keywords: vertex operator algebras
zbMATH Keywords: twisted modules
MaRDI profile type: Publication
OpenAlex ID: W2106115819
arXiv ID: 0905.0514
cites work: A \(\mathbb{Z}_{2}\)-orbifold model of the symplectic fermionic vertex operator superalgebra
cites work: Logarithmic intertwining operators and W(2,2p−1) algebras
cites work: On the triplet vertex algebra \(\mathcal W(p)\)
cites work: Lattice construction of logarithmic modules for certain vertex algebras
cites work: ALGEBRAIC ASPECTS OF ORBIFOLD MODELS
cites work: Characters and modular properties of permutation orbifolds
cites work: Q5702383
cites work: Twisted sectors for tensor product vertex operator algebras associated to permutation groups
cites work: An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras
cites work: Vertex algebras, Kac-Moody algebras, and the Monster
cites work: SYSTEMATIC APPROACH TO CYCLIC ORBIFOLDS
cites work: Nonmeromorphic operator product expansion andC2-cofiniteness for a family of -algebras
cites work: The operator algebra of orbifold models
cites work: Beauty and the beast: Superconformal symmetry in a monster module
cites work: Q3973923
cites work: Twisted modules for vertex algebras associated with even lattices
cites work: The algebraic structure of relative twisted vertex operators
cites work: Twisted representations of vertex operator algebras
cites work: Modular-invariance of trace functions in orbifold theory and generalized Moonshine.
cites work: Q4435788
cites work: TWISTED VERTEX OPERATORS AND BERNOULLI POLYNOMIALS
cites work: Kazhdan-Lusztig correspondence for the representation category of the triplet \(W\)-algebra in logarithmic CFT
cites work: Logarithmic extensions of minimal models: characters and modular transformations
cites work: Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
cites work: On modular invariant partition functions of conformal field theories with logarithmic operators.
cites work: On fusion rules in logarithmic conformal field theories
cites work: Logarithmic torus amplitudes
cites work: Fermionic expressions for the characters of \(c_{p,1}\) logarithmic conformal field theories
cites work: On axiomatic approaches to vertex operator algebras and modules
cites work: A natural representation of the Fischer-Griess Monster with the modular function J as character
cites work: Q3804868
cites work: Q3994993
cites work: Nonsemisimple fusion algebras and the Verlinde formula
cites work: Orbifolds by cyclic permutations in Gepner type superstrings and in the corresponding Calabi-Yau manifolds
cites work: The logarithmic triplet theory with boundary
cites work: From boundary to bulk in logarithmic CFT
cites work: Radford, Drinfeld and Cardy boundary states in the (1,p) logarithmic conformal field models
cites work: THE GENERAL TWISTED OPEN WZW STRING
cites work: TWO LARGE EXAMPLES IN ORBIFOLD THEORY: ABELIAN ORBIFOLDS AND THE CHARGE CONJUGATION ORBIFOLD ON ${\mathfrak{su}}(n)$
cites work: A LOGARITHMIC GENERALIZATION OF TENSOR PRODUCT THEORY FOR MODULES FOR A VERTEX OPERATOR ALGEBRA
cites work: Symplectic fermions
cites work: Calculus of twisted vertex operators
cites work: Q3810803
cites work: Integrable boundary conditions and {\cal W} -extended fusion in the logarithmic minimal models {\cal LM}(1\hbox{,}\, p)
DOI: 10.1007/S00220-010-0999-6
description: scientific article