E. Gillaspy

activity

20152021

most citedSeparable representations of higher-rank graphs

2 citations · 3 across the 4 of their papers we have counts for

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15 papers · 1 filter

math.OA2021

Irreducibility and monicity for representations of $k$ -graph $C^{*}$ -algebras

Carla Farsi, Elizabeth Gillaspy, Daniel Gonçalves

The representations of a $k$ -graph $C^{*}$ -algebra $C^{*} (Λ)$ which arise from $Λ$ -semibranching function systems are closely linked to the dynamics of the $k$ -graph $Λ$ . In this paper…

math.OA2020

Analyzing the Weyl construction for dynamical Cartan subalgebras

A. Duwenig, E. Gillaspy, R. Norton

When the reduced twisted $C^{*}$ -algebra $C_{r}^{*} (G, c)$ of a non-principal groupoid $G$ admits a Cartan subalgebra, Renault's work on Cartan subalgebras implies th…

math.OA2020★ 1 cited

Moves on $k$ -graphs preserving Morita equivalence

Caleb Eckhardt, Kit Fieldhouse, Daniel Gent +3

We initiate the program of extending to higher-rank graphs ( $k$ -graphs) the geometric classification of directed graph $C^{*}$ -algebras, as completed in the 2016 paper of Eilers, Res…

math.OA2020

Cartan subalgebras for non-principal twisted groupoid $C^{*}$ -algebras

Anna Duwenig, Elizabeth Gillaspy, Rachael Norton +2

Renault proved in 2008 that if $G$ is a topologically principal groupoid, then $C_{0} (G^{(0)})$ is a Cartan subalgebra in $C_{r}^{*} (G, Σ)$ for any twist $Σ$ over $G$ . However, there are…

math.OA2018

Generalized gauge actions on $k$ -graph $C^{*}$ -algebras: KMS states and Hausdorff structure

Carla Farsi, Elizabeth Gillaspy, Nadia S. Larsen +1

For a finite, strongly connected $k$ -graph $Λ$ , an Huef, Laca, Raeburn and Sims studied the KMS states associated to the preferred dynamics of the $k$ -graph $C^{*}$ -algebra $C^{*} (Λ)$ .…

math.OA2018

Isomorphism of the cubical and categorical cohomology groups of a higher-rank graph

Elizabeth Gillaspy, Jianchao Wu

We use category-theoretic techniques to provide two proofs showing that for a higher-rank graph $Λ$ , its cubical (co-)homology and categorical (co-)homology groups are isomorphic i…

Irreducibility and monicity for representations of k-graph C∗-algebras

Analyzing the Weyl construction for dynamical Cartan subalgebras

Moves on k-graphs preserving Morita equivalence

Cartan subalgebras for non-principal twisted groupoid C∗-algebras

Generalized gauge actions on k-graph C∗-algebras: KMS states and Hausdorff structure

Isomorphism of the cubical and categorical cohomology groups of a higher-rank graph

Irreducibility and monicity for representations of $k$ -graph $C^{*}$ -algebras

Moves on $k$ -graphs preserving Morita equivalence

Cartan subalgebras for non-principal twisted groupoid $C^{*}$ -algebras

Generalized gauge actions on $k$ -graph $C^{*}$ -algebras: KMS states and Hausdorff structure