Twisted modules for toroidal vertex algebras

Fei Kong; Haisheng Li; Shaobin Tan; Qing Wang

doi:10.1016/j.jpaa.2015.09.002

Twisted modules for toroidal vertex algebras

Fei Kong
, Haisheng Li
, Shaobin Tan
, Qing Wang

Rutgers Camden, Mathematics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

Abstract

This is a paper in a series systematically to study toroidal vertex algebras and their (twisted) modules. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that most of the extended affine Lie algebras can be associated to toroidal vertex algebras.

Original language	American English
Pages (from-to)	1681-1706
Number of pages	26
Journal	Journal of Pure and Applied Algebra
Volume	220
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2015.09.002
State	Published - 2016

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2015.09.002

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abstract = "This is a paper in a series systematically to study toroidal vertex algebras and their (twisted) modules. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that most of the extended affine Lie algebras can be associated to toroidal vertex algebras.",

author = "Fei Kong and Haisheng Li and Shaobin Tan and Qing Wang",

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T1 - Twisted modules for toroidal vertex algebras

AU - Kong, Fei

AU - Li, Haisheng

AU - Tan, Shaobin

AU - Wang, Qing

PY - 2016

Y1 - 2016

N2 - This is a paper in a series systematically to study toroidal vertex algebras and their (twisted) modules. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that most of the extended affine Lie algebras can be associated to toroidal vertex algebras.

AB - This is a paper in a series systematically to study toroidal vertex algebras and their (twisted) modules. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that most of the extended affine Lie algebras can be associated to toroidal vertex algebras.

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 5

ER -

Twisted modules for toroidal vertex algebras

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