Rationality of W-algebras: principal nilpotent cases
By T. Arakawa. 2012
133 citations recorded by the source corpus.
We prove the rationality of all the minimal series principal W -algebras discovered by Frenkel, Kac and Wakimoto, thereby giving a new family of rational and C2-conite vertex operator algebras. A key ingredient in our proof is the study of Zhu’s algebra of simple W -algebras via the quantized Drinfeld-Sokolov reduction. We show that the functor of taking Zhu’s algebra commutes with the reduction functor. Using this general fact we determine the maximal spectrums of the associated graded of Zhu’s algebras of vertex operator algebras associated with admissible representations of ane Kac-Moody algebras as well.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/084a90126d4f1b722af7254ec7491d6e193328e6
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Cosets of affine vertex algebras inside larger structures (2014, unknown): “oincideswithasimplerationalW-algebraoftypeggivenbytheDrinfeld-Sokolovreduction associated to the principal embedding of sl2 in g[FF, FKW]. The rationality of these W-algebras was proven by Arakawa in [Ara], and this conjecture was recently proven in full generality in a joint work with Arakawa [ACL]”
- Fusion categories for affine vertex algebras at admissible levels (2018, background): “Since the W -algebra is rational [20] so that its module category is modular [1] the map from the Grothendieck ring to the endomorphism ring of the direct sum of all simples via open Hopf links is an isomorphism and so it follows that Lk(λ, 0)⊠ Lk(0, λ ′) ∼= Lk(λ, λ ′).”