2015/10/31 by Uwe Franz, Anna Kula, Adam Skalski
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Compact quantum group #Discrete mathematics #Mathematics #Noncommutative geometry #Permutation (music) #Permutation group #Physics #Pure mathematics #Quantum #Quantum algorithm #Quantum dynamics #Quantum group #Quantum mechanics #Quantum operation #Quantum probability #Quantum process #Random Matrices and Applications #math.PR #math.QA #msc:17B37 #msc:43A05 #msc:46L65
paper · pdf · doi:10.1007/978-3-319-29116-1_11
60 pages
openalex publication_date 2016/01/01 · arxiv created 2016/03/08 · arxiv updated 2016/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.