Galois reconstruction of finite quantum groups

1999/06/15 by Julien Bichon, Bichon, Julien
Mathematics · #16W30 #18D10 #46L89 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:16W30 #msc:18D10 #msc:46L89

paper · pdf · doi:10.48550/arxiv.math/9906103

Latex, 10 pages

arxiv created 1999/06/15 · openalex publication_date 1999/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a finite-dimensional Hopf algebra from the category of finite-dimensional measured comodule algebras.

Related

• Quantum group coproducts and universality under scalar extensions
• The global quantum duality principle: theory, examples, applications
• Simple modules over finite quantum groups and their Drinfel'd doubles
• Equivariant Tannaka-Krein reconstruction and quantum automorphism groups of discrete structures
• Residually finite quantum group algebras