Quantum automorphism groups of finite quantum groups are classical

Paweł Kasprzak; Piotr M. Sołtan; Stanisław L. Woronowicz

doi:10.1016/j.geomphys.2014.12.006

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arXiv · 1410.1404

Quantum automorphism groups of finite quantum groups are classical

Paweł Kasprzak·Piotr M. Sołtan·Stanisław L. Woronowicz

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Abstract

In a recent paper of Bhowmick, Skalski and So{\l}tan the notion of a quantum group of automorphisms of a finite quantum group was introduced and, for a given finite quantum group G, existence of the universal quantum group acting on G by automorphisms was proved. We show that this universal quantum group is in fact a classical group. The key ingredient of the proof is the use of multiplicative unitary operators, and we include a thorough discussion of this notion in the context of finite quantum groups.

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Paweł Kasprzak, Piotr M. Sołtan, Stanisław L. Woronowicz. 2014-10-06. Quantum automorphism groups of finite quantum groups are classical. https://doi.org/10.1016/j.geomphys.2014.12.006

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