Regularity of fixed-point vertex operator subalgebras

2016/03/17 by Carnahan, Scott, Miyamoto, Masahiko · 1 citation
#11F22 #17B69 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1603.05645

Abstract

We show that if T is a simple non-negatively graded regular vertex operator algebra with a nonsingular invariant bilinear form and σ is a finite order automorphism of T, then the fixed-point vertex operator subalgebra T^σ is also regular. This yields regularity for fixed point vertex operator subalgebras under the action of any finite solvable group. As an application, we obtain an SL₂(ℤ)-compatibility between twisted twining characters for commuting finite order automorphisms of holomorphic vertex operator algebras. This resolves one of the principal claims in the Generalized Moonshine conjecture.

Cited by

• Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

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• Regularity of certain vertex operator algebras with two generators
• Regularity of rational vertex operator algebras
• Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
• Lattice subalgebras of strongly regular vertex operator algebras
• Twisted regular representations and bimodules in vertex operator algebra theory