Results 1 to 10 of about 347,643 (299)
Topological spaces associated to higher-rank graphs [PDF]
Journal of Combinatorial Theory, Series A, 2016 We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying ...
Aidan Sims +4 more
core +9 more sources
Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs [PDF]
SciPost Physics, 2023 We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D
Hiromi Ebisu, Bo Han
doaj +5 more sources
A dual graph construction for higher-rank graphs, and $K$-theory for finite 2-graphs [PDF]
Proceedings of the American Mathematical Society, 2004 Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide.
Allen, Stephen, Pask, David, Sims, Aidan
core +9 more sources
Cohn path algebras of higher-rank graphs [PDF]
Algebras and Representation Theory, 2016 In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph $\Lambda $, there exists a higher-rank graph $T\Lambda $ such that the Cohn path algebra of $\Lambda $ is isomorphic to the Kumjian-Pask algebra
Clark, Lisa Orloff +1 more
core +2 more sources
On twisted higher-rank graph 𝐶*-algebras [PDF]
Transactions of the American Mathematical Society, 2015 We define the categorical cohomology of a k k -graph Λ \Lambda and show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative characterisation of the twisted k k -graph C
Kumjian, Alex +2 more
openaire +5 more sources
Refinement of Higher-Rank Graph Reduction [PDF]
, 2022 Given a row-finite, source-free, graph of rank k, we extend the definition of reduction introduced by Eckhardt et al. This constitutes a large step forward in the extension of the geometric classification of finite directed graph $C^*$-algebras presented by Eilers et al. to higher-rank graph $C^*$-algebras.
S. Joseph Lippert
openaire +4 more sources
Simplicity of C*-algebras associated to higher-rank graphs [PDF]
Bulletin of the London Mathematical Society, 2007 We prove that if is a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if is cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) is equivalent to a suitably modified version of Robertson and Steger's original nonperiodicity condition (H3) which in particular involves only ...
Robertson, David, Sims, Aidan
openaire +6 more sources
Separable representations of higher-rank graphs [PDF]
, 2017 In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^*$-algebras associated to strongly connected finite $k$-graphs $ $. We begin with the representations associated to the $ $-semibranching function systems introduced by Farsi, Gillaspy, Kang, and Packer in \cite{FGKP},
Farsi, Carla +4 more
openaire +3 more sources
The stable exotic Cuntz algebras are higher-rank graph algebras [PDF]
Proceedings of the American Mathematical Society, Series B, 2023 For each odd integer n ≥ 3 n \geq 3 , we construct a rank-3 graph Λ n \Lambda _n with involution γ n \gamma _n whose real C ∗ C^* -algebra C
Boersema, Jeffrey L. +2 more
openaire +3 more sources
Orbit equivalence of higher-rank graphs [PDF]
Journal of Operator Theory, 2021 We study the notion of continuous orbit equivalence of finitely-aligned higher-rank graphs. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic.
Carlsen, Toke Meier, Rout, James
openaire +3 more sources