45 citations · 139 across the 19 of their papers we have counts for
28 papers · 1 filter
Laplace operators on quantum graphs
Arkadiusz Bochniak, Dawid Jasiński, Paweł Kasprzak
We introduce a class of Laplace operators associated with quantum graphs in the operator-system framework. To this end, we investigate structural properties of quantum graphs relat…
Quantum Mycielskians: symmetries, twin vertices and distinguishing labelings
Arkadiusz Bochniak, Igor Chełstowski, Paweł Kasprzak +1
We investigate a quantum generalization of the Mycielski construction for quantum graphs. In particular, we analyze the quantum symmetries of quantum Mycielskians and their relatio…
Quantum correlations on quantum spaces
Arkadiusz Bochniak, Paweł Kasprzak, Piotr M. Sołtan
For given quantum (non-commutative) spaces and we study the quantum space of maps from to .…
Noncommutative Furstenberg boundary
Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski +1
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out…
Kawada-Itô-Kelley Theorem for Quantum Semigroups
Paweł Kasprzak, Fatemeh Khosravi, Piotr M. Sołtan
Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with c…
Shifts of group-like projections and contractive idempotent functionals for locally compact quantum groups
Paweł Kasprzak
A one to one correspondence between shifts of group-like projections on a locally compact quantum group which are preserved by the scaling group and contractive idem…
The Lattice of Idempotent States on a Locally Compact Quantum Group
Paweł Kasprzak, Piotr M. Sołtan
We study lattice operations on the set of idempotent states on a locally compact quantum group corresponding to the operations of intersection of compact subgroups and forming the…
Group-like projections for locally compact quantum groups
Ramin Faal, Paweł Kasprzak
Let be a locally compact quantum group. We give a 1-1 correspondence between group-like projections in preserved by the scaling group and idempo…
Induction for locally compact quantum groups revisited
Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski +1
In this paper we revisit the theory of induced representations in the setting of locally compact quantum groups. In the case of induction from open quantum subgroups, we show that…
Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations
Kenny De Commer, Paweł Kasprzak, Adam Skalski +1
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space in…
Hopf images in locally compact quantum groups
Paweł Józiak, Paweł Kasprzak, Piotr M. Sołtan
This manuscript is devoted to the study of the concept of a generating subset (a.k.a. Hopf image of a morphism) in the setting of locally compact quantum groups. The aim of this pa…
Coideals, quantum subgroups and idempotent states
Pawel Kasprzak, Fatemeh Khosravi
We establish a one to one correspondence between idempotent states on a locally compact quantum group G and integrable coideals in the von Neumann algebra of bounded measurable fun…
Integrable actions and quantum subgroups
Paweł Kasprzak, Fatemeh Khosravi, Piotr M. Sołtan
We study homomorphisms of locally compact quantum groups from the point of view of integrability of the associated action. For a given homomorphism of quantum groups $Π\colon\mathb…
Open quantum subgroups of locally compact quantum groups
Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski
The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusion…
The canonical central exact sequence for locally compact quantum groups
Paweł Kasprzak, Adam Skalski, Piotr M. Sołtan
For a locally compact quantum group we define its center, , and its quantum group of inner automorphisms, . We show…
Quantum families of quantum group homomorphisms
Mariusz Budziński, Paweł Kasprzak
The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additiona…
Quantum groups with projection and extensions of locally compact quantum groups
P. Kasprzak, P. M. Sołtan
The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensi…
Braided quantum SU(2) groups
Paweł Kasprzak, Ralf Meyer, Sutanu Roy +1
We construct a family of q-deformations of SU(2) for complex parameters q not equal to 0. For real q, the deformation coincides with Woronowicz' compact quantum SU_q(2) group. For…
Quantum automorphism groups of finite quantum groups are classical
Paweł Kasprzak, Piotr M. Sołtan, Stanisław L. Woronowicz
In a recent paper of Bhowmick, Skalski and Sołtan the notion of a quantum group of automorphisms of a finite quantum group was introduced and, for a given finite quantum group G, e…
Quantum groups with projection on von Neumann algebra level
Paweł Kasprzak, Piotr M. Sołtan
We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introdu…
Rieffel deformation of tensor functor and braided quantum groups
Pawel Kasprzak
In this paper we apply Rieffel deformation to C*- tensor product viewed as a functor on the category of C*-algebras with an abelian group action. In the case of the Rieffel deforma…
Embeddable Quantum Homogeneous Spaces
Paweł Kasprzak, Piotr M. Sołtan
We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we find an interesting…
Closed quantum subgroups of locally compact quantum groups
Matthew Daws, Paweł Kasprzak, Adam Skalski +1
We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions - one due to S.Vaes and one due to S.L.Woronowicz - are anal…
Rieffel Deformation of Homogeneous Spaces
P. Kasprzak
Let H be a closed subgroup of a locally compact group G and let X=G/H be the quotient space of left cosets. Let C*X be the corresponding G-C*-algebra of continuous functions on X,…