Related papers: The socle and semisimplicity of a Kumjian-Pask alg…

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…

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…

For any Kumjian-Pask algebra $KP_R(\Lambda)$ defined over a $k$-graph $\Lambda$ of a special kind (a "standard $k$-graph"), we obtain an $R$-basis.

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 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 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.

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…

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…

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 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…

In this paper we introduce the class of graded Poisson color algebras as the natural generalization of graded Poisson algebras and graded Poisson superalgebras. For $\Lambda$ an arbitrary abelian group, we show that any of such…

In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not contain neither…

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…

Given a row-finite higher-rank $k$-graph $\Lambda$, we define a commutative monoid $T_\Lambda$ which is a higher-rank analogue of the talented monoid of a directed graph. The talented monoid $T_\Lambda$ is canonically a…

We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the…

We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in N. We focus on semigroups P arising as part of a quasi-lattice ordered group (G,P) in the sense of…