Exchange Relations for Finite Type Cluster Algebras with Acyclic Initial Seed and Principal Coefficients

TL;DR

This paper provides a detailed explicit description of all exchange relations in finite type cluster algebras with acyclic initial seeds and principal coefficients, enhancing understanding of their algebraic structure.

Contribution

It offers a comprehensive explicit characterization of exchange relations in a specific class of finite type cluster algebras, which was previously not fully detailed.

Findings

Explicit exchange relations for all finite type cluster algebras with acyclic seeds

Clarification of the algebraic structure of these cluster algebras

Facilitation of further algebraic and combinatorial analysis

Abstract

We give an explicit description of all the exchange relations in any finite type cluster algebra with acyclic initial seed and principal coefficients.