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

2019/02/21 by Megumi Kitagawa, Kitagawa, Megumi
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1902.07893

openalex publication_date 2019/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Compact quantum ergodic systems

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