A characterization of freeness by invariance under quantum spreading

DOI10.1515/CRELLE.2011.066zbMath1241.46038arXiv1002.4390MaRDI QIDQ3096795

Stephen Curran

Publication date: 14 November 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4390

zbMATH Keywords

exchangeabilityfree probabilityde Finetti theoremspreadabilityquantum increasing sequencequantum spreading

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) General quantum mechanics and problems of quantization (81S99) Quantizations, deformations for selfadjoint operator algebras (46L65) Exchangeability for stochastic processes (60G09)

Related Items

Quantum Bernstein’s theorem and the hyperoctahedral quantum group ⋮ Markovianity and the Thompson monoid \(F^+\) ⋮ Introduction to compact (matrix) quantum groups and Banica-Speicher (easy) quantum groups ⋮ Noncommutative homogeneous spaces: the matrix case ⋮ Extended de Finetti theorems for boolean independence and monotone independence ⋮ Tail algebras for monotone and \(q\)-deformed exchangeable stochastic processes ⋮ QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS ⋮ On the classification of easy quantum groups ⋮ De Finetti theorems for easy quantum groups ⋮ Quantum invariant families of matrices in free probability ⋮ De Finetti theorems for the unitary dual group

Cites Work

• A noncommutative extended de Finetti theorem
• Integration over quantum permutation groups
• Quantum families of maps and quantum semigroups on finite quantum spaces
• A noncommutative de Finetti theorem: invariance under quantum permutations is equivalent to freeness with amalgamation
• Compact matrix pseudogroups
• Quantum symmetry groups of finite spaces
• Quantum exchangeable sequences of algebras