Prime and primitive Kumjian-Pask algebras

  title={Prime and primitive Kumjian-Pask algebras},
  author={Maryam Kashoul-Radjabzadeh and Hossein Larki and Abdolmohammad Aminpour},
  journal={arXiv: Rings and Algebras},
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 quotient $k$-graphs, these results describe prime and primitive graded basic ideals of Kumjian-Pask algebras. In particular, when $\Lambda$ is strongly aperiodic and $R$ is a field, all prime and primitive ideals of a Kumjian-Pask algebra $\mathrm{KP}_R… 

Simple Modules for Kumjian-Pask Algebras

The paper introduces the notion of a representation k-graph (∆, α) for a given k-graph Λ. It is shown that any representation k-graph for Λ yields a module for the Kumjian-Pask algebra KP(Λ), and the

Primitive ideal space of higher-rank graph C⁎-algebras and decomposability

  • H. Larki
  • Mathematics, Computer Science
    Journal of Mathematical Analysis and Applications
  • 2019



Kumjian-Pask algebras of higher-rank graphs

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

The module type of a ring

Aperiodicity and primitive ideals of row-finite k-graphs

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