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Lévy Processes on Quantum Permutation Groups

  • Uwe FranzEmail author
  • Anna Kula
  • Adam Skalski
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)

Abstract

We describe basic motivations behind quantum or noncommutative probability, introduce quantum Lévy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups. The first half of this paper is a survey on quantum probability, compact quantum groups, and Lévy processes on compact quantum groups. In the second half the theory is applied to quantum permutations groups. Explicit examples are constructed and certain classes of such Lévy processes are classified.

Keywords

Compact quantum group free permutation group (quantum) Lévy process 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Département de mathématiques de BesançonUniversité de Franche-ComtéBesançon cedexFrance
  2. 2.Instytut MatematycznyUniwersytet Wrocławski, WrocławPoland
  3. 3.Institute of Mathematics of the Polish Academy of Sciences WarszawaPoland

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