# Prime and primitive Kumjian-Pask algebras

@article{KashoulRadjabzadeh2015PrimeAP, title={Prime and primitive Kumjian-Pask algebras}, author={Maryam Kashoul-Radjabzadeh and Hossein Larki and Abdolmohammad Aminpour}, journal={arXiv: Rings and Algebras}, year={2015} }

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…

## 2 Citations

### Simple Modules for Kumjian-Pask Algebras

- MathematicsAlgebras and Representation Theory
- 2022

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

- Mathematics, Computer ScienceJournal of Mathematical Analysis and Applications
- 2019

## References

SHOWING 1-10 OF 18 REFERENCES

### Kumjian-Pask algebras of higher-rank graphs

- Mathematics
- 2011

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…

### Aperiodicity and primitive ideals of row-finite k-graphs

- Mathematics, Computer Science
- 2012

This work describes the primitive ideal space of the C*-algebra of a row-finite k-graph with no sources when every ideal is gauge invariant and proves some new results on aperiodicity.

### HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2003

Abstract We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies to…

### The Leavitt path algebras of arbitrary graphs

- Mathematics
- 2008

We extend the notion of the Leavitt path algebra of a graph to include all directed graphs. We show how various ring-theoretic properties of these more general structures relate to the corresponding…

### Nonstable K-theory for Graph Algebras

- Mathematics
- 2004

We compute the monoid V(LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and…

### Removing sources from higher-rank graphs

- Mathematics
- 2006

For a higher-rank graph $\Lambda$ with sources we detail a construction that creates a higher-rank graph $\bar{\Lambda}$ that does not have sources and contains $\Lambda$ as a subgraph. Furthermore,…