6 papers
Shift equivalence relations through the lens of C*-correspondences
Boris Bilich, Adam Dor-On, Efren Ruiz
We continue the study of shift equivalence relations from the perspective of C*-bimodule theory. We study emerging shift equivalence relations following work of the second-named au…
A New Geometric Morita Invariant for Higher Rank Graph -algebras
Mackenzie Amann, Liam Gallagher, Rachael Norton +1
Higher rank graphs, also known as -graphs, are a -dimensional generalization of directed graphs and a rich source of examples of -algebras. In the present paper, we cont…
Unital aligned shift equivalence and the graded classification conjecture for Leavitt path algebras
Kevin Aguyar Brix, Adam Dor-On, Roozbeh Hazrat +1
We prove that a unital shift equivalence induces a graded isomorphism of Leavitt path algebras when the shift equivalence satisfies an alignment condition. This yields another step…
Equivariant homotopy classification of graph C*-algebras
Boris Bilich, Adam Dor-On, Efren Ruiz
We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first e…
The Algebraic Kirchberg-Phillips Question for Leavitt path algebras
Efren Ruiz
The Algebraic Kirchberg-Phillips Question for Leavitt path algebras asks whether unital -theory is a complete isomorphism invariant for unital, simple, purely infinite Leavitt p…
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…