Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 695-707, 2022

Remarks on Sekine quantum groups

Jialei Chen, Shilin Yang

Received March 25, 2021. Published online February 14, 2022.

Abstract: We first describe the Sekine quantum groups $\mathcal{A}_k$ (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of $\mathcal{A}_k$ and describe their representation rings $r(\mathcal{A}_k)$. Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of $r(\mathcal{A}_k)$.

Keywords: Sekine quantum group; representation ring; Casimir number

Classification MSC: 16T05, 16D70, 16G10

DOI: 10.21136/CMJ.2022.0112-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Jialei Chen, Shilin Yang (corresponding author), College of Mathematics, Faculty of Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China, e-mail: chenjialei@bjut.edu.cn, slyang@bjut.edu.cn

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