The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity

2009/02/26 by Kiyokazu Nagatomo, Akihiro Tsuchiya, Nagatomo, K. +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0902.4607

openalex publication_date 2009/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the abelian category of the modules over triplet VOA W(p) is category equivalent to the abelian category of the modules over quantum algebra of type sl₂ at root of unity.

Citations

• Classification of irreducible modules of certain subalgebras of free boson vertex algebra

Cited by

• The unrolled quantum group inside Lusztig's quantum group of divided\n powers
• Ambidextrous objects and trace functions for nonsemisimple categories
• Hopf and Frobenius algebras in conformal field theory
• A matrix realization of the quantum group g_{p, q}
• Tensor Categories arising from the Virasoro Algebra

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• Module categories over representations of SL_q(2) and graphs