Monoids, dynamics and Leavitt path algebras

Gene Abrams; Roozbeh Hazrat

doi:10.1016/j.exmath.2025.125684

Monoids, dynamics and Leavitt path algebras

Gene Abrams, Roozbeh Hazrat

University of Colorado Colorado Springs

Research output: Contribution to journal › Article › peer-review

2 Downloads (Pure)

Abstract

Leavitt path algebras, which are algebras associated to directed graphs, were first introduced about 20 years ago. They have strong connections to such topics as symbolic dynamics, operator algebras, non-commutative geometry, representation theory, and even chip firing. In this article we invite the reader to sneak a peek at these fascinating algebras and their interplay with several seemingly disparate parts of mathematics.

Original language	English
Article number	125684
Number of pages	17
Journal	Expositiones Mathematicae
Volume	43
Issue number	5
DOIs	https://doi.org/10.1016/j.exmath.2025.125684
Publication status	Published - Sept 2025

Keywords

Abelian sandpile model
C-algebra
Leavitt path algebra
Sandpile monoid
Symbolic dynamics

Access to Document

10.1016/j.exmath.2025.125684Licence: CC BY

Full textFinal published version, 585 KBLicence: CC BY

Cite this

@article{b9f7dcc38f224b7ea91905e8e3c2eb80,

title = "Monoids, dynamics and Leavitt path algebras",

abstract = "Leavitt path algebras, which are algebras associated to directed graphs, were first introduced about 20 years ago. They have strong connections to such topics as symbolic dynamics, operator algebras, non-commutative geometry, representation theory, and even chip firing. In this article we invite the reader to sneak a peek at these fascinating algebras and their interplay with several seemingly disparate parts of mathematics.",

keywords = "Abelian sandpile model, C-algebra, Leavitt path algebra, Sandpile monoid, Symbolic dynamics",

author = "Gene Abrams and Roozbeh Hazrat",

year = "2025",

month = sep,

doi = "10.1016/j.exmath.2025.125684",

language = "English",

volume = "43",

journal = "Expositiones Mathematicae",

issn = "0723-0869",

publisher = "Elsevier GmbH",

number = "5",

}

TY - JOUR

T1 - Monoids, dynamics and Leavitt path algebras

AU - Abrams, Gene

AU - Hazrat, Roozbeh

PY - 2025/9

Y1 - 2025/9

N2 - Leavitt path algebras, which are algebras associated to directed graphs, were first introduced about 20 years ago. They have strong connections to such topics as symbolic dynamics, operator algebras, non-commutative geometry, representation theory, and even chip firing. In this article we invite the reader to sneak a peek at these fascinating algebras and their interplay with several seemingly disparate parts of mathematics.

AB - Leavitt path algebras, which are algebras associated to directed graphs, were first introduced about 20 years ago. They have strong connections to such topics as symbolic dynamics, operator algebras, non-commutative geometry, representation theory, and even chip firing. In this article we invite the reader to sneak a peek at these fascinating algebras and their interplay with several seemingly disparate parts of mathematics.

KW - Abelian sandpile model

KW - C-algebra

KW - Leavitt path algebra

KW - Sandpile monoid

KW - Symbolic dynamics

UR - http://www.scopus.com/inward/record.url?scp=105004728274&partnerID=8YFLogxK

U2 - 10.1016/j.exmath.2025.125684

DO - 10.1016/j.exmath.2025.125684

M3 - Article

AN - SCOPUS:105004728274

SN - 0723-0869

VL - 43

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 5

M1 - 125684

ER -

Monoids, dynamics and Leavitt path algebras

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this