Woronowicz's Tannaka-Krein duality and free orthogonal quantum groups

2016/02/15 by Sara Malacarne, Malacarne, Sara · 2 citations
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1602.04807

openalex publication_date 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite dimensional Hilbert space H and a collection of operators between its tensor powers satisfying certain properties, we give a category-free proof of the existence of a compact quantum group G with a fundamental representation U on H such that the intertwiners between the tensor powers of U coincide with the given collection of operators. We then explain how the general version of Woronowicz's Tannaka-Krein duality can be deduced from this.

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• Partition C*-algebras II - Links to Compact Matrix Quantum Groups
• Principles of operator algebras

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