Results 11 to 20 of about 347,643 (299)
von Neuman algebras of strongly connected higher-rank graphs [PDF]
Mathematische Annalen, 2014 We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz--Krieger algebra of a strongly connected finite $k$-graph. For inverse temperatures above 1, all of the extremal KMS states are of
Laca, Marcelo +4 more
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Kumjian–Pask algebras of locally convex higher-rank graphs [PDF]
Journal of Algebra, 2014 Minor changes made.
Clark, Lisa Orloff +2 more
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Amenability of Groupoids Arising from Partial Semigroup Actions and Topological Higher Rank Graphs [PDF]
, 2015 We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if there is countable
Renault, Jean N., Williams, Dana P.
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The path space of a higher-rank graph [PDF]
Studia Mathematica, 2011 30 pages, all figures drawn with TikZ/PGF. Updated numbering and minor corrections to coincide with published version. Updated 29-Feb-2012 to fix a compiling error which resulted in the arXiv PDF output containing two copies of the ...
Samuel B. G. Webster
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Asymptotic -Algebras from -Actions on Higher Rank Graphs [PDF]
Abstract and Applied Analysis, 2013 For a dynamical system arising from -action on a higher rank graph with finite vertex set, we show that the semidirect product of the asymptotic equivalence relation groupoid is essentially principal if and only if the -graph satisfies the aperiodic ...
Inhyeop Yi
doaj +2 more sources
Higher rank graph C*-algebras [PDF]
, 2000 14 pages, see also http://nyjm.albany.edu:8000/j/2000/6-1nf ...
Kumjian, Alex, Pask, David
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Product systems of graphs and the Toeplitz algebras of higher-rank graphs [PDF]
, 2003 There has recently been much interest in the $C^*$-algebras of directed graphs. Here we consider product systems $E$ of directed graphs over semigroups and associated $C^*$-algebras $C^*(E)$ and $\mathcal{T}C^*(E)$ which generalise the higher-rank graph algebras of Kumjian-Pask and their Toeplitz analogues. We study these algebras by constructing from $
Raeburn, Iain, Sims, Aidan
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Aperiodicity and cofinality for finitely aligned higher-rank graphs [PDF]
, 2009 We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs \Lambda, and prove that C*(\Lambda) is simple if and only if \Lambda is aperiodic and cofinal.
Lewin, Peter, Sims, Aidan
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Kumjian–Pask algebras of finitely aligned higher-rank graphs [PDF]
Journal of Algebra, 2017 We extend the the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and have a graded uniqueness theorem. We also prove the Cuntz-Kreiger uniqueness theorem; to do this, we use a groupoid approach.
Lisa Orloff Clark +1 more
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Higher rank graphs, k-subshifts and k-automata [PDF]
, 2018 Given a $k$-graph $ $ we construct a Markov space $M_ $, and a collection of $k$ pairwise commuting cellular automata on $M_ $, providing for a factorization of Markov's shift. Iterating these maps we obtain an action of ${\mathbb N}^k$ on $M_ $ which is then used to form a semidirect product groupoid $M_ \rtimes {\mathbb N}^k$.
Exel, R., Steinberg, B.
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