Regular vertex operator subalgebras and compressions of intertwining operators

Abstract

Let $V$ be a vertex operator subalgebra of $U$. Assume that $U$, $V$, and its commutant $V^c$ in $U$ are CFT-type, self-dual, and regular VOAs. Assume also that the double commutant $V^{cc}$ equals $V$. We prove that any intertwining operator of $V$ is a compression of intertwining operators of $U$.

arXiv comment15 pages, final revision, to appear in J. Algebra

References in corpus (15)

• Modular invariance of trace functions in orbifold theory
• W-algebras as coset vertex algebras
• Rationality of W-algebras: principal nilpotent cases
• From vertex operator algebras to conformal nets and back
• Full field algebras
• Fusion of Positive Energy Representations of LSpin(2n)
• Tensor categories and the mathematics of rational and logarithmic conformal field theory
• Rationality, Regularity, and C_2-cofiniteness
• Categorical extensions of conformal nets
• Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I
• Representation theory in chiral conformal field theory: from fields to observables
• Construction of the unitary free fermion Segal CFT
• Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras
• Fusion and positivity in chiral conformal field theory
• Unbounded field operators in categorical extensions of conformal nets

Cited by in corpus (1)

• Unbounded field operators in categorical extensions of conformal nets