Introduction to Cluster Algebras. Chapters 1-3

TL;DR

This paper introduces the foundational concepts of cluster algebras, covering total positivity, mutations, and the structure of clusters and seeds, serving as an initial draft for a comprehensive textbook on the subject.

Contribution

It provides an organized presentation of the basic principles and structures of cluster algebras in the early chapters of a forthcoming textbook.

Findings

Explains total positivity in the context of cluster algebras

Describes mutations of quivers and matrices

Defines clusters and seeds in the algebraic framework

Abstract

This is a preliminary draft of Chapters 1-3 of our forthcoming textbook "Introduction to Cluster Algebras." This installment contains: Chapter 1. Total positivity Chapter 2. Mutations of quivers and matrices Chapter 3. Clusters and seeds