On ultragraph Leavitt path algebras with finite Gelfand-Kirillov dimension

Abstract

In this article, we prove that every ultragraph Leavitt path algebra is a direct limit of Leavitt path algebras of finite graphs and determine the Gelfand-Kirillov dimension of an ultragraph Leavitt path algebra. We also characterize ultragraph Leavitt path algebras whose simple modules are finitely presented, and show that these algebras have finite Gelfand-Kirillov dimension. Moreover, we construct new classes of simple modules over ultragraph Leavitt path algebras associated with minimal infinite emitters and minimal sinks, which have not appeared in the context of Leavitt path algebras of graphs.

KEYWORDS:

• Gelfand-Kirillov dimension
• simple module
• ultragraph Leavitt path algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16P90
• 16D70
• 16S88

Acknowledgments

The authors are extremely grateful to the anonymous referees for very careful reading of the manuscript and a number of comments which helped to improve the presentation.

Additional information

Funding

The authors were supported by the International Center of Research and Postgraduate Training in Mathematics under grant ICRTM03-2021.01.