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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…
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…