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of 112
pro vyhledávání: '"Brownlowe, Nathan"'
We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the k-graph embeds in its fundamental groupoid, this AF algebra is a Fell
Externí odkaz:
http://arxiv.org/abs/2403.01337
We study group actions on multitrees, which are directed graphs in which there is at most one directed path between any two vertices. In our main result we describe a six-term exact sequence in $K$-theory for the reduced crossed product $C_0(\partial
Externí odkaz:
http://arxiv.org/abs/2311.05285
Autor:
Brownlowe, Nathan, Buss, Alcides, Gonçalves, Daniel, Hume, Jeremy B., Sims, Aidan, Whittaker, Michael F.
We extend Nekrashevych's $KK$-duality for $C^*$-algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a graph, removing the recurrence condition entirely and generalising from
Externí odkaz:
http://arxiv.org/abs/2302.03989
Autor:
Brownlowe, Nathan, Robertson, David
We introduce the notion of self-similarity for compact quantum groups. For a finite set $X$, we introduce a $C^*$-algebra $\mathbb{A}_X$, which is the quantum automorphism group of the infinite homogeneous rooted tree $X^*$. Self-similar quantum grou
Externí odkaz:
http://arxiv.org/abs/2302.01552
Publikováno v:
J. Noncommut. Geom. 18 (2024), 265--312
We consider Deaconu--Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*-algebra of such a groupoid determined by a continuous
Externí odkaz:
http://arxiv.org/abs/2109.02583
We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal Nica--Toeplitz and Cun
Externí odkaz:
http://arxiv.org/abs/1910.02472
We study the internal structure of $C^*$-algebras of right LCM monoids by means of isolating the core semigroup $C^*$-algebra as the coefficient algebra of a Fock-type module on which the full semigroup $C^*$-algebra admits a left action. If the semi
Externí odkaz:
http://arxiv.org/abs/1902.02674
We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections. We also show that if E has no sinks, then we can recover E
Externí odkaz:
http://arxiv.org/abs/1812.08903
Akademický článek
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Autor:
Armstrong, Becky, Brownlowe, Nathan
Publikováno v:
J. Math. Anal. Appl. 466 (2018), 1443--1475
We use product systems of $C^*$-correspondences to introduce twisted $C^*$-algebras of topological higher-rank graphs. We define the notion of a continuous $\mathbb{T}$-valued $2$-cocycle on a topological higher-rank graph, and present examples of su
Externí odkaz:
http://arxiv.org/abs/1706.09358