Twisted modules for affine vertex algebras over fields of prime characteristic

Haisheng Li, Qiang Mu

Research output: Contribution to journalArticle

Abstract

In this paper, twisted modules for modular affine vertex algebras V(ℓ,0) and for their quotient vertex algebras V χ(ℓ,0) with g a restricted Lie algebra are studied. Let σ be an automorphism of g and let T be a positive integer relatively prime with the characteristic p such that σT=1. It is proved that [Formula presented]-graded irreducible σ-twisted V 0(ℓ,0)-modules are in one-to-one correspondence with irreducible modules for the restricted enveloping algebra u(g0), where g0 is the subalgebra of σ-fixed points in g. It is also proved that when g=h is abelian, the twisted Heisenberg Lie algebra hˆ[σ] is actually isomorphic to the untwisted Heisenberg Lie algebra hˆ, unlike in the case of characteristic zero. Furthermore, for any nonzero level ℓ, irreducible σ-twisted L(ℓ,0)-modules are explicitly classified and the complete reducibility of every σ-twisted L(ℓ,0)-module is obtained.

Original languageEnglish (US)
Pages (from-to)380-414
Number of pages35
JournalJournal of Algebra
Volume541
DOIs
StatePublished - Jan 1 2020

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Vertex Algebra
Module
Heisenberg Algebra
Lie Algebra
Irreducible Module
Relatively prime
Enveloping Algebra
Reducibility
One to one correspondence
Automorphism
Subalgebra
Quotient
Isomorphic
Fixed point
Integer
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Twisted module
  • Vertex operator algebra

Cite this

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Twisted modules for affine vertex algebras over fields of prime characteristic. / Li, Haisheng; Mu, Qiang.

In: Journal of Algebra, Vol. 541, 01.01.2020, p. 380-414.

Research output: Contribution to journalArticle

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