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Kac-Paljutkin Quantum Group as a Quantum Subgroup of the quantum SU(2)

Kitagawa Megumi

Commentationes Mathematicae

2019

Vol. 59, No. 1/2

47--61

We show that the Kac-Paljutkin Hopf algebra appears as a quotient of C(SU-1 (2)), which means that the corresponding quantum group GKP can be regarded as a quantum subgroup of SU-1 (2). We combine the fact that corepresentation category of the Kac-Paljutkin Hopf algebra is a Tambara-Yamagami tensor category associated with the Krein 4-group and the method of graded twisting of Hopf algebras, to construct the Hopf ∗-homomorphism.