Examples of solvable and nilpotent finite quantum groups

2024/02/01 by Gerard Glowacki, Glowacki, Gerard, Masamune Hattori +3
Mathematics · #16T05 #16T10 #16T25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2402.00706

openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups and we classify the solvable series of Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem. Some semisimple quasitriangular Hopf algebras of dimensions 2pq are also studied. In Appendix A, we give a direct computation of the universal R-matrices for Kac--Paljutkin's 8-dimensional finite quantum group.

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