Minimal W-algebras of \mathfrakso_N at level minus one

2025/06/18 by Thomas Creutzig, Creutzig, Thomas, Justine Fasquel +7
Computer Science · Mathematics · #Advanced Algebra and Logic #Rings, Modules, and Algebras #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2506.15605

Abstract

For N ∈\mathbb Z_{≥ 7} we show that the simple minimal W-algebra of \mathfrakso_N at level minus one is isomorphic to the even subalgebra of the tensor product of the simple affine vertex superalgebra of \mathfrakosp_1|2 at level (N-6)/(2) with N-4 free fermions. In particular when N is even this minimal W-algebra is strongly rational as conjectured by Arakawa-Moreau.

Citations

• Rigidity of non-negligible objects of moderate growth in braided categories
• Resolving Verlinde's formula of logarithmic CFT
• Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
• Building blocks for W-algebras of classical types
• On lisse non-admissible minimal and principal W-algebras
• Weight representations of affine Kac-Moody algebras and small quantum groups
• On rationality for C₂-cofinite vertex operator algebras
• Rationality and Fusion Rules of Exceptional W-Algebras
• W-algebras with non-admissible levels and the Deligne exceptional series
• Rigidity and modularity of vertex tensor categories
• Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture

Related

• Minimal W-algebras with non-admissible levels and intermediate Lie algebras
• Supersymmetries in the theory of W-algebras
• Linearization of W algebras and W superalgebras
• Free Field Realization of Supersymmetric W-algebras
• Spectral flow and application to unitarity of representations of minimal W-algebras