Geodesic
Remarks on Sekine quantum groups
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 695-707
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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 $r(\mathcal {A}_{k})$.
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 $r(\mathcal {A}_{k})$.
DOI : 10.21136/CMJ.2022.0112-21
Classification : 16D70, 16G10, 16T05
Keywords: Sekine quantum group; representation ring; Casimir number 
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Chen, Jialei; Yang, Shilin. Remarks on Sekine quantum groups. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 695-707. doi: 10.21136/CMJ.2022.0112-21

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