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Related papers: Twisted modules for quantum vertex algebras

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Twisted current algebras are fixed point subalgebras of current algebras under a finite group action. Special cases include equivariant map algebras and twisted forms of current algebras. Their finite-dimensional simple modules fall into…

Representation Theory · Mathematics 2017-08-17 Jean Auger , Michael Lau

We associate quantum vertex algebras and their $\phi$-coordinated quasi modules to certain deformed Heisenberg algebras.

Quantum Algebra · Mathematics 2011-06-17 Haisheng Li

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…

Quantum Algebra · Mathematics 2016-06-17 Bojko Bakalov

In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…

Quantum Algebra · Mathematics 2016-12-22 Hongyan Guo , Qing Wang

We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of…

Quantum Algebra · Mathematics 2024-05-08 Lucia Bagnoli , Slaven Kožić

We extend the geometric approach to vertex algebras developed by the first author to twisted modules, allowing us to treat orbifold models in conformal field theory. Let $V$ be a vertex algebra, $H$ a finite group of automorphisms of $V$,…

Algebraic Geometry · Mathematics 2007-05-23 Edward Frenkel , Matthew Szczesny

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

Quantum Algebra · Mathematics 2007-05-23 Benjamin Doyon , James Lepowsky , Antun Milas

We introduce and study twist vertex operators for a (lower-bounded generalized) twisted modules for a grading-restricted vertex (super)algebra. We prove duality, weak associativity, a Jacobi identity, a generalized commutator formula,…

Quantum Algebra · Mathematics 2019-08-28 Yi-Zhi Huang

We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.

Quantum Algebra · Mathematics 2007-05-23 Haisheng Li

Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…

Quantum Algebra · Mathematics 2021-03-05 Bojko Bakalov , Samantha Kirk

A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…

Quantum Algebra · Mathematics 2013-12-18 Kenichiro Tanabe

A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…

Algebraic Geometry · Mathematics 2015-03-18 Bernard Le Stum , Adolfo Quirós

We consider a class of weak modules for vertex operator algebras that we call logarithmic modules. We also construct nontrivial examples of intertwining operators between certain logarithmic modules for the Virasoro vertex operator algebra.…

Quantum Algebra · Mathematics 2007-05-23 Antun Milas

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the…

Quantum Algebra · Mathematics 2009-10-31 K. Barron , C. Dong , G. Mason

We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…

Representation Theory · Mathematics 2010-02-12 Yuly Billig , Michael Lau

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…

Representation Theory · Mathematics 2024-11-27 Asghar Daneshvar , Hajar Kiamehr , Maryam Yazdanifar , Malihe Yousofzadeh

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

Quantum Algebra · Mathematics 2007-05-23 S. Berman , Y. Billig , J. Szmigielski

We study a twisted version of module algebras called module Hom-algebras. It is shown that module algebras deform into module Hom-algebras via endomorphisms. As an example, we construct certain q-deformations of the usual sl(2)-action on…

Rings and Algebras · Mathematics 2008-12-31 Donald Yau

In this paper, we construct an irreducible vertex module for twisted affine Lie algebra of type A_{2l}^{(2)}.

Representation Theory · Mathematics 2008-11-04 Limeng Xia , Naihong Hu , Xiaotang Bai

We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…

Quantum Algebra · Mathematics 2007-05-23 Matthew Szczesny