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arXiv · 1902.07893

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

Megumi Kitagawa
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Abstract

We show that the Kac-Paljutkin Hopf algebra appears as a quotient of $C(SU_{-1}(2))$, which means that the corresponding quantum group $G_{KP}$ 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.

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Megumi Kitagawa. 2019-02-21. Kac-Paljutkin Quantum Group as a Quantum Subgroup of the Quantum SU(2). https://arxiv.org/abs/1902.07893

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