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$K$-theory and homotopies of 2-cocycles on transformation groups

This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid…
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Finite decomposition rank for virtually nilpotent groups

We show that inductive limits of virtually nilpotent groups have strongly quasidiagonal C*-algebras, extending results of the first author on solvable virtually nilpotent groups. We use this result…
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Irreducible representations of nilpotent groups generate classifiable C*-algebras

We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with…
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Wavelets and Graph C ∗ -Algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph C∗-algebras, including the higher-rank graph C∗-algebras of A. Kumjian and D. Pask. Many authors…
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Wavelets and spectral triples for fractal representations of Cuntz algebras

In this article we provide an identification between the wavelet decompositions of certain fractal representations of $C^*-$algebras of directed graphs of M. Marcolli and A. Paolucci, and the…
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K-theory and homotopies of 2-cocycles on higher-rank graphs

This paper continues our investigation into the question of when a homotopy of 2-cocycles on a locally compact Hausdorff groupoid gives rise to an isomorphism of the K-theory groups of the twisted…
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K-theory for twisted groupoid C*-algebras

This thesis constitutes the first steps in the author’s program to investigate the question of when a homotopy of 2-cocycles ω = {ωt}t∈[0,1] on a locally compact Hausdorff groupoid G induces an…
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Separable representations, KMS states, and wavelets for higher-rank graphs

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Spectral triples and wavelets for higher-rank graphs

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Monic representations of finite higher-rank graphs

In this paper, we define the notion of monic representation for the $C^{\ast }$-algebras of finite higher-rank graphs with no sources, and we undertake a comprehensive study of them. Monic…
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