56 citations · 364 across the 42 of their papers we have counts for
48 papers
Naimark's Problem for graph C*-algebras and Leavitt path algebras
Kulumani M. Rangaswamy, Mark Tomforde
We describe how boundary paths in a graph can be used to construct irreducible representations of the associated graph C*-algebra and the associated Leavitt path algebra. We use th…
Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence
Gene Abrams, Efren Ruiz, Mark Tomforde
Let and be finite graphs with no sinks, and any field. We show that shift equivalence of the adjacency matrices and , together with an additional compatibili…
A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras
Menevşe Eryüzlü, Mark Tomforde
We introduce a property of C*-correspondences, which we call Condition (S), to serve as an analogue of Condition (L) of graphs. We use Condition (S) to prove a Cuntz-Krieger Unique…
Morita equivalence for graded rings
Gene Abrams, Efren Ruiz, Mark Tomforde
The classical Morita Theorem for rings established the equivalence of three statements, involving categorical equivalences, isomorphisms between corners of finite matrix rings, and…
Matricial Archimedean order unit spaces and quantum correlations
Roy Araiza, Travis Russell, Mark Tomforde
We introduce a matricial analogue of an Archimedean order unit space, which we call a -AOU space. We develop the category of -AOU spaces and -positive maps and exhibit fun…
A Universal Representation for Quantum Commuting Correlations
Roy Araiza, Travis Russell, Mark Tomforde
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundam…