18 citations · 42 across the 19 of their papers we have counts for
21 papers
Voltage quantum graphs and a Gross-Tucker theorem for quantum graphs
Björn Schäfer, Mariusz Tobolski
A voltage graph is a finite directed graph whose edges are labeled by elements of a finite group . A classical construction of Gross and Tucker associates to every voltage graph…
On morphisms of topological quivers
Mariusz Tobolski
We introduce regular morphisms of topological quivers and show that they give rise to a subcategory of the category of topological quivers and quiver morphisms. Our regularity cond…
Gluing topological graph C*-algebras
Atul Gothe, John Quigg, Mariusz Tobolski
We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topolo…
Principal Actions on Topological Quivers and Associated Operator Dynamics
Matthew Gillespie, Lucas Hall, Benjamin Jones +1
We study topological quivers admitting a free and proper action by a locally compact group together with their associated -algebras. On the topological side, we provid…
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…
The covariant functoriality of graph algebras
Piotr M. Hajac, Mariusz Tobolski
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain…
Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras
Isabelle Baraquin, Uwe Franz, Malte Gerhold +2
We find a finite free resolution of the counit of the free unitary quantum groups of van Daele and Wang and, more generally, Bichon's universal cosovereign Hopf algebras with a gen…
Non-commutative classifying spaces of groups via quasi-topologies and pro--algebras
Alexandru Chirvasitu, Mariusz Tobolski
For a locally compact Hausdorff topological group , we construct a universal pro--algebra as the non-commutative geometer's analogue of the total space of th…
From length-preserving pushouts of graphs to one-surjective pullbacks of graph algebras
Piotr M. Hajac, Mariusz Tobolski
The unions of directed graphs are the simplest examples of pushouts of directed graphs. The conditions under which they contravariantly induce surjective gauge-equivariant pullback…
Noncommutative numerable principal bundles from group actions on C*-algebras
Mariusz Tobolski
We introduce a definition of the locally trivial -C*-algebra, which is a noncommutative counterpart of the total space of a locally compact Hausdorff numerable principal -bun…
Graph algebras
Piotr M. Hajac, Mariusz Tobolski
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length in a graph with edges and no loops. Our proof relies o…
Non-surjective pullbacks of graph C*-algebras from non-injective pushouts of graphs
Alexandru Chirvasitu, Piotr M. Hajac, Mariusz Tobolski
We find a substantial class of pairs of -homomorphisms between graph C*-algebras of the form whose pullback C*-algebra is…
Equivariant Dimensions of Graph C*-algebras
Alexandru Chirvasitu, Benjamin Passer, Mariusz Tobolski
We explore the recently introduced local-triviality dimensions by studying gauge actions on graph -algebras, as well as the restrictions of the gauge action to finite cyclic s…
Pullbacks of graph C*-algebras from admissible pushouts of graphs
Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski
We define an admissible decomposition of a graph into subgraphs and , and consider the intersection graph as a subgraph of both and . We pro…
Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces
Francesca Arici, Piotr M. Hajac, Mariusz Tobolski
By a diagonal embedding of in , we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere to the -action on the prolong…
A graded pullback structure of Leavitt path algebras of trimmable graphs
Piotr M. Hajac, Atabey Kaygun, Mariusz Tobolski
Motivated by recent results in graph C*-algebras concerning an equivariant pushout structure of the Vaksman-Soibelman quantum odd spheres, we introduce a class of graphs called tri…
The local-triviality dimension of actions of compact quantum groups
Eusebio Gardella, Piotr M. Hajac, Mariusz Tobolski +1
We define the local-triviality dimension for actions of compact quantum groups on unital C*-algebras. The resulting compact quantum principal bundle is said to be locally trivial w…
An equivariant pullback structure of trimmable graph C*-algebras
Francesca Arici, Francesco D'Andrea, Piotr M. Hajac +1
We prove that the graph C*-algebra of a trimmable graph is -equivariantly isomorphic to a pullback C*-algebra of a subgraph C*-algebra and the C*-alge…
Renormalization group procedure for potential
Sebastian M. Dawid, Rafał Gonsior, Jan Kwapisz +3
Schrödinger equation with potential exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r…
The weak Hilbert-Smith conjecture from a Borsuk-Ulam-type conjecture
Alexandru Chirvasitu, Ludwik Dąbrowski, Mariusz Tobolski
We prove a number of results surrounding the Borsuk-Ulam-type conjecture of Baum, Dąbrowski and Hajac (BDH, for short), to the effect that given a free action of a compact group $G…
Lie-Hamilton systems on curved spaces: A geometrical approach
Francisco J. Herranz, Javier de Lucas, Mariusz Tobolski
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a -dependent vector field taking values in a fin…