Idempotent states on Sekine quantum groups

2018/09/08 by Haonan Zhang, Zhang, Haonan
Mathematics · #15A24 #20G42 #60B15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1809.02798

openalex publication_date 2018/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sekine quantum groups are a family of finite quantum groups. The main result of this paper is to compute all the idempotent states on Sekine quantum groups, which completes the work of Franz and Skalski. This is achieved by solving a complicated system of equations using linear algebra and basic number theory. From this we discover a new class of non-Haar idempotent states. The order structure of the idempotent states on Sekine quantum groups is also discussed. Finally we give a sufficient condition for the convolution powers of states on Sekine quantum group to converge.

Citations

• Random Walks on Finite Quantum Groups: Diaconis-Shahshahani Theory for Quantum Groups

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