2 citations · 7 across the 20 of their papers we have counts for
22 papers
Actions of quantum groups on dual operator spaces and their crossed products
Jason Crann, Joeri De Ro, Jacek Krajczok
We study the category of dual operator spaces equipped with an action of a locally compact quantum group . The Fubini crossed product functor $-\rtimes^\mathcal{F} \mat…
Scaling automorphisms of compact quantum groups
Jacek Krajczok
In this short article we verify the conjecture proposed by P. M. Sołtan and the author, by proving that a second countable compact quantum group whose scaling automorphisms are inn…
Crossed product functors associated to -pseudofunctions
Jacek Krajczok, Ebrahim Samei, Timo Siebenand +1
We show that the -pseudofunctions, which were recently shown to lead to exotic completions of group -algebras by Wiersma and the second named author, can be used to co…
Braided quantum group - a case study
Jacek Krajczok, Piotr. M. Sołtan
We continue the study of the braided compact quantum group for complex satisfying introduced by Kasprzak, Meyer, Roy and Woronowicz (J. Noncommut.…
The standard construction for cocycle twisted and braided tensor product W-algebras
K. De Commer, J. Krajczok
Given a locally compact quantum group and a (generalized) dual unitary -cocycle , any W-algebra with a -action can be twisted into a new…
Asymptotic invariants for fusion algebras associated with compact quantum groups
Jacek Krajczok, Adam Skalski
We introduce and study certain asymptotic invariants associated with fusion algebras (equipped with a dimension function), which arise naturally in the representation theory of com…
Braided tensor product of von Neumann algebras
Kenny De Commer, Jacek Krajczok
We introduce a definition of braided tensor product of von Neumann algebras equipped with an action of a quasi-triangular qua…
Cowling-Haagerup constant of the product of discrete quantum groups
Jacek Krajczok
We show that (central) Cowling-Haagerup constant of discrete quantum groups is multiplicative, which extends the result of Freslon to general (not necesarilly unimodular) discrete…
The Covariant Stone-von Neumann Theorem for Locally Compact Quantum Groups
Lucas Hall, Leonard Huang, Jacek Krajczok +1
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimate…
Averaging multipliers on locally compact quantum groups
Matthew Daws, Jacek Krajczok, Christian Voigt
We study an averaging procedure for completely bounded multipliers on a locally compact quantum group with respect to a compact quantum subgroup. As a consequence we show that cent…
On certain invariants of compact quantum groups
Jacek Krajczok, Piotr M. Sołtan
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mai…
Separation properties for positive-definite functions on locally compact quantum groups and for associated von Neumann algebras
Jacek Krajczok, Adam Skalski
Using Godement mean on the Fourier-Stieltjes algebra of a locally compact quantum group we obtain strong separation results for quantum positive-definite functions associated to a…
The approximation property for locally compact quantum groups
Matthew Daws, Jacek Krajczok, Christian Voigt
We study the Haagerup--Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus--Ruan and Crann. Along the way we discuss h…
Examples of compact quantum groups with a factor
Jacek Krajczok, Piotr M. Sołtan
For each we exhibit an uncountable family of compact quantum groups such that the von Neumann algebra is the…
On the von Neumann algebra of class functions on a compact quantum group
Jacek Krajczok, Mateusz Wasilewski
We study analogues of the radial subalgebras in free group factors (called the algebras of class functions) in the setting of compact quantum groups. For the free orthogonal quantu…
Compact quantum group structures on type-I -algebras
Alexandru Chirvasitu, Jacek Krajczok, Piotr M. Sołtan
We prove a number of results having to do with equipping type-I -algebras with compact quantum group structures, the two main ones being that such a compact quantum g…
Modular properties of type I locally compact quantum groups
Jacek Krajczok
The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related to the modular theory of the Haar integrals on $\mathbb{…
The quantum disk is not a quantum group
Jacek Krajczok, Piotr M. Sołtan
We show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz C*-algebra does not admit any compact quantum group structure. We prove that if such a structure…
Coamenability of type I locally compact quantum groups
Jacek Krajczok
We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operator…
Symmetry of eigenvalues of operators associated with representations of compact quantum groups
Jacek Krajczok
We ask the question whether for a given unitary representation the associated operator has spectrum invariant under inversion -- in th…
Compact quantum groups with representations of bounded degree
Jacek Krajczok, Piotr M. Sołtan
We show that a compact quantum group all whose irreducible representations have dimension bounded by a fixed constant must be of Kac type, in other words, its Haar measure is a tra…
Center of the algebra of functions on the quantum group and related topics
Jacek Krajczok, Piotr M. Sołtan
The center of the algebra of continuous functions on the quantum group is determined as well as centers of other related algebras. Several other results concerning this q…