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arXiv · 2402.00706

Examples of solvable and nilpotent finite quantum groups

Gerard Glowacki·Masamune Hattori·Masato Tanaka
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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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Gerard Glowacki, Masamune Hattori, Masato Tanaka. 2024-02-01. Examples of solvable and nilpotent finite quantum groups. https://arxiv.org/abs/2402.00706

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