Results 21 to 30 of about 347,643 (299)
Applications of entropy of product systems: Higher-rank graphs [PDF]
Linear Algebra and its Applications, 2020 We consider C*-algebras of finite higher-rank graphs along with their rotational action. We show how the entropy theory of product systems with finite frames applies to identify the phase transitions of the dynamics. We compute the positive inverse temperatures where symmetry breaks, and in particular we identify the subharmonic parts of the gauge ...
Evgenios T. A. Kakariadis
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Twisted C*-algebras associated to finitely aligned higher-rank graphs [PDF]
Documenta Mathematica, 2014 We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties.
Sims, Aidan +2 more
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Monic representations of finite higher-rank graphs [PDF]
Ergodic Theory and Dynamical Systems, 2018 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 representations are the representations that, when restricted to the commutative$C^{\ast }$-algebra of the continuous functions on the infinite path space, admit a ...
FARSI, CARLA +4 more
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Gauge-invariant ideals in the C*-algebras of finitely aligned higher-rank graphs [PDF]
, 2004 We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant.
Sims, Aidan
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Higher rank lamplighter groups are graph automatic [PDF]
Journal of Algebra, 2018 We show that the higher rank lamplighter groups, or Diestel-Leader groups $ _d(q)$ for $d \geq 3$, are graph automatic. This introduces a new family of graph automatic groups which are not automatic.
Bérubé, Sophie +2 more
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Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs [PDF]
, 2003 We define the relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs. We prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem for relative Cuntz-Krieger algebras.Comment: 16 ...
Sims, Aidan
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A generalized Cuntz–Krieger uniqueness theorem for higher-rank graphs [PDF]
Journal of Functional Analysis, 2014 We present a uniqueness theorem for k-graph C*-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k-graph C*-algebra, it is sufficient that the representation be injective on a distinguished abelian C*-subalgebra.
Brown, Jonathan H. +2 more
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Wavelets and spectral triples for higher-rank graphs [PDF]
, 2017 In this paper, we present two new ways to associate a spectral triple to a higher-rank graph $ $. Moreover, we prove that these spectral triples are intimately connected to the wavelet decomposition of the infinite path space of $ $ which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015.
Farsi, Carla +4 more
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A GENERALISATION OF HIGHER-RANK GRAPHS
Bulletin of the Australian Mathematical Society, 2021 AbstractWe introduce ‘generalised higher-rank k-graphs’ as a class of categories equipped with a notion of size. They extend not only higher-rank k-graphs, but also the Levi categories introduced by the first author as a categorical setting for graphs of groups.
MARK V. LAWSON, ALINA VDOVINA
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Spectral triples for higher-rank graph $C^*$-algebras [PDF]
MATHEMATICA SCANDINAVICA, 2020 In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(\Lambda )$ of a strongly connected finite higher-rank graph Λ. Our spectral triple builds on an approach used by Consani and Marcolli to construct spectral triples for Cuntz-Krieger algebras.
Farsi, Carla +4 more
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