Modular properties of type I locally compact quantum groups

2020/06/04 by Jacek Krajczok, Krajczok, Jacek
Mathematics · Physics and Astronomy · #20G42 (primary) #22D10 (secondary) #46L51 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2006.02746

openalex publication_date 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related to the modular theory of the Haar integrals on \mathbbG and \widehat\mathbbG act on the level of direct integrals. Using these results we derive a web of implications between properties such as unimodularity or traciality of the Haar integrals. We also study in detail two examples: discrete quantum group \widehatSU_q(2) and the quantum az+b group.

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