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Quantum Families of Invertible Maps and Related Problems

  Published:2016-03-10
 Printed: Jun 2016
  • Adam Skalski,
    Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00--956 Warszawa, Poland
  • Piotr Sołtan,
    Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Poland
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Abstract

The notion of families of quantum invertible maps (C$^*$-algebra homomorphisms satisfying Podleś' condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In particular Wang's quantum automorphism groups are shown to be universal with respect to quantum families of invertible maps. Further the construction of the Hopf image of Banica and Bichon is phrased in the purely analytic language and employed to define the quantum subgroup generated by a family of quantum subgroups or more generally a family of quantum invertible maps.
Keywords: quantum families of invertible maps, Hopf image, universal quantum group quantum families of invertible maps, Hopf image, universal quantum group
MSC Classifications: 46L89, 46L65 show english descriptions Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
Quantizations, deformations
46L89 - Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
46L65 - Quantizations, deformations
 

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