The kumjian-pask algebras of finite finitely aligned k-graphs without cycle as modules

Sumanang Gozali,Rizky Rosjanuardi,Isnie Yusnitha,Ade Gafar Abdullah,Asep Bayu Dani Nandiyanto

doi:10.1051/matecconf/201819701003

Sumanang Gozali, Rizky Rosjanuardi + Show 3 more

Open Access

https://doi.org/10.1051/matecconf/201819701003

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Abstract

In general, every algebra can be viewed as a module over itself. In this paper, we analyze the structure of Kumjian-Pask algebras of finite finitely aligned k-graph without cycles via module theory.

Highlights

For a directed graph E, it can be constructed, in general, the corresponding graph algebra
In 2005, Gene Abrams and Aranda Pino [2] introduced the Leavitt path algebra for a directed graph, which can be viewed as an algebraic analogue of the graph algebra
Larki obtained a characterization for a finite-dimensional Kumjian-Pask Algebra [7]

Summary

Introduction

For a directed graph E, it can be constructed, in general, the corresponding graph algebra. Many important results on this topic have been published by researchers. In 2005, Gene Abrams and Aranda Pino [2] introduced the Leavitt path algebra for a directed graph, which can be viewed as an algebraic analogue of the graph algebra. For a k-graph Λ, one may interested in the corresponding algebra and obtains many important results. Many researchers have studied this topic for the cases row-finite without sources, locally convex, and finitely aligned k-graph [3]. [4] introduced this algebra and called it Kumjian-Pask Algebra, for the row-finite Λ without sources. In [6], L.O. Clark and Pangalela published their results for finitely aligned kgraph. Larki obtained a characterization for a finite-dimensional Kumjian-Pask Algebra [7]

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