2013/12/13 by Sven Raum, Raum, Sven, Moritz Weber +1 · 1 citation
Mathematics · #05E10 #16T30 (Secondary) #46L54 #46L65 (Primary) #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Random Matrices and Applications #math.OA #math.QA #msc:05E10 #msc:16T30 #msc:46L54 #msc:46L65
paper · pdf · doi:10.48550/arxiv.1312.3857
38 pages
arxiv created 2013/12/13 · openalex publication_date 2013/12/13 · arxiv updated 2013/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1987, Woronowicz gave a definition of compact matrix quantum groups generalizing compact Lie groups in the setting of noncommutative geometry. About twenty years later, Banica and Speicher isolated a class of compact matrix quantum groups with an intrinsic combinatorial structure. These so called easy quantum groups are determined by categories of partitions. They have been proven useful in order to understand various aspects of quantum groups, in particular linked with Voiculescu's free probability theory. Furthermore, they exhibit a way to find examples of compact quantum groups besides q-deformations and quantum isometry groups. These characteristics naturally motivated attempts to fully classify them. This is completed in the present article.