scholarly journals Inductive limits of compact quantum groups and their unitary representations

2021 ◽  
Vol 111 (5) ◽  
Author(s):  
Ryosuke Sato
Keyword(s):  
Quantum Groups ◽  
Unitary Representations ◽  
Inductive Limits ◽  
Compact Quantum Groups

scholarly journals Weak mixing for locally compact quantum groups

2016 ◽  
Vol 37 (5) ◽  
pp. 1657-1680 ◽  
Author(s):  
AMI VISELTER
Keyword(s):  
Quantum Groups ◽  
Von Neumann Algebras ◽  
Unitary Representations ◽  
Discrete Groups ◽  
Weak Mixing ◽  
Locally Compact ◽  
Von Neumann ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups ◽  
Weakly Mixing

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the non-commutative Jacobs–de Leeuw–Glicksberg splitting theorem of Runde and the author [Ergodic theory for quantum semigroups. J. Lond. Math. Soc. (2) 89(3) (2014), 941–959]. Furthermore, a relation between mixing and weak mixing of state-preserving actions of discrete quantum groups and the properties of certain inclusions of von Neumann algebras, which is known for discrete groups, is demonstrated.

scholarly journals The Haagerup property for locally compact quantum groups

2016 ◽  
Vol 2016 (711) ◽  
Author(s):  
Matthew Daws ◽  
Pierre Fima ◽  
Adam Skalski ◽  
Stuart White
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Unitary Representations ◽  
Compact Groups ◽  
Locally Compact ◽  
Haagerup Property ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups ◽  
Dual Quantum

AbstractThe Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established. In particular it is shown that a locally compact quantum group 𝔾 has the Haagerup property if and only if its mixing representations are dense in the space of all unitary representations. For discrete 𝔾 we characterise the Haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group

scholarly journals On cocycle twisting of compact quantum groups

2010 ◽  
Vol 258 (10) ◽  
pp. 3362-3375 ◽  
Author(s):  
Kenny De Commer
Keyword(s):  
Quantum Groups ◽  
Compact Quantum Groups

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

scholarly journals A new characterisation of idempotent states on finite and compact quantum groups

2009 ◽  
Vol 347 (17-18) ◽  
pp. 991-996 ◽  
Author(s):  
Uwe Franz ◽  
Adam Skalski
Keyword(s):  
Quantum Groups ◽  
Compact Quantum Groups

scholarly journals An averaging trick for smooth actions of compact quantum groups on manifolds

2015 ◽  
Vol 46 (4) ◽  
pp. 477-488 ◽  
Author(s):  
Debashish Goswami ◽  
Soumalya Joardar
Keyword(s):  
Quantum Groups ◽  
Compact Quantum Groups
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