The relationship between skew group algebras and orbifold theory

2001/07/24 by Gaywalee Yamskulna, Yamskulna, Gaywalee
Mathematics · Physics and Astronomy · #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B69

paper · pdf · doi:10.48550/arxiv.math/0107180

15 pages. To appear in Journal of Algebra

openalex publication_date 2001/07/24 · arxiv created 2002/04/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V. In [DY], it was shown that any irreducible V-module is a completely reducible V^G-module where V^G is the G-invariant sub-vertex operator algebra of V. In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V-module when g is in the center of G and V is a g-rational vertex operator algebra.

Citations

• The radical of a vertex operator algebra associated to a module

Related

• On Orbifold Theory
• Orbifold theory for vertex algebras and Galois correspondence
• Super orbifold theory
• On the operator content of nilpotent orbifold models
• Twisted representations of vertex operator superalgebras