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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.

Super-easy quantum groups : definition and examples

Banica T.

Bulletin of the Polish Academy of Sciences. Mathematics

2018

Vol. 66, no. 1

57--68

We investigate the “two-parameter” quantum symmetry groups that we previously constructed with Skalski, with the conclusion that some of these quantum groups, namely those without singletons, are “super-easy” in a suitable sense, which we axiomatize here. Our formalism also covers the symplectic group Spn and its free version Sp+n, and some other interesting examples. Finally, we address the general problem of classifying the super-easy quantum groups, and we make a few comments on it.

One-sided quantum quasigroups and loops

Smith J. D. H.

Demonstratio Mathematica

2015

Vol. 48, nr 4

620--636

Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. This paper examines their one-sided analogues, which are not self-dual. Just as quantum quasigroups are the “quantum” version of quasigroups, so one-sided quantum quasigroups are the “quantum” version of left or right quasigroups.