The Leavitt Path Algebras of Ultragraphs

Mostafa Imanfar; Abdolrasoul Pourabbas∗; Hossein Larki

doi:10.5666/KMJ.2020.60.1.21

Article

Kyungpook Mathematical Journal 2020; 60(1): 21-43

Published online March 31, 2020

The Leavitt Path Algebras of Ultragraphs

Mostafa Imanfar and Abdolrasoul Pourabbas∗, Hossein Larki

Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran e-mail : m.imanfar@aut.ac.ir and arpabbas@aut.ac.ir
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran e-mail : h.larki@scu.ac.ir

Abstract

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Abstract

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.

Keywords: ultragraph C^∗,-algebra, Leavitt path algebra, Exel-Laca algebra.