相关论文: Bases for Kumjian-Pask algebras over standard $k$-…

In this paper, prime as well as primitive Kumjian-Pask algebras $\mathrm{KP}_R(\Lambda)$ of a row-finite $k$-graph $\Lambda$ over a unital commutative ring $R$ are completely characterized in graph-theoretic and algebraic terms. By applying…

The paper introduces the notion of a representation $k$-graph $(\Delta,\alpha)$ for a given $k$-graph $\Lambda$. It is shown that any representation $k$-graph for $\Lambda$ yields a module for the Kumjian-Pask algebra $KP(\Lambda)$, and the…

The Kumjian-Pask algebra KP(\Lambda) is a graded algebra associated to a higher-rank graph \Lambda and is a generalization of the Leavitt path algebra of a directed graph. We analyze the minimal left-ideals of KP(\Lambda), and identify its…

The Kumjian-Pask algebras are path algebras associated to higher-rank graphs, and generalize the Leavitt path algebras. We study the center of simple Kumjian-Pask algebras and characterize commutative Kumjian-Pask algebras.

Given any finitely aligned higher-rank graph $\Lambda$ and any unital commutative ring $R$, the Kumjian-Pask algebra $\mathrm{KP}_R(\Lambda)$ is known as the higher-rank generalization of Leavitt path algebras. After characterizing simple…

Let $\Lambda$ be a row-finite higher-rank graph with no sources. We identify a maximal commutative subalgebra $\mathcal{M}$ inside the Kumjian-Pask algebra ${\rm KP}_R(\Lambda)$. We also prove a generalized Cuntz-Krieger uniqueness theorem…

We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze their ideal structure.

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…

The Kumjian-Pask algebra of a higher-rank graph generalises the Leavitt path algebra of a directed graph. We extend the definition of Kumjian-Pask algebra to row-finite higher-rank graphs $\Lambda$ with sources which satisfy a…

This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…

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…

In this paper, we characterize properly purely infinite Steinberg algebras $A_K(\mathcal{G})$ for strongly effective, ample Hausdorff groupoids $\mathcal{G}$. As an application, when $\Lambda$ is a strongly aperiodic $k$-graph, we show that…

To a higher rank directed graph $(\Lambda, d)$, in the sense of Kumjian and Pask, one can associate natural noncommutative analytic Toeplitz algebras, both weakly closed and norm closed. We introduce methods for the classification of these…

We give a vertex set description for basic, graded, regular ideals of locally-convex Kumjian-Pask Algebras. We also show that Condition (B) is preserved when taking the quotient by a basic, graded, regular ideal. We further show that when a…

We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our…

We prove that if \Lambda is a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if \Lambda is cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) is equivalent to a…

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. We use this…

We initiate the study of real $C^*$-algebras associated to higher-rank graphs $\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify a spectral sequence which computes the $\mathcal{CR}$ $K$-theory of…

A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct…

We introduce the Exel-Pardo $*$-algebra $\mathrm{EP}_R(G,\Lambda)$ associated to a self-similar $k$-graph $(G,\Lambda,\varphi)$. We prove the $\mathbb{Z}^k$-graded and Cuntz-Krieger uniqueness theorems for such algebras and investigate…