TL;DR
This paper explores the connections between Ptolemy's theorem and various identities in cluster algebras, highlighting their diverse applications across mathematical fields.
Contribution
It provides an overview of the relationships between Ptolemy relations and identities in cluster algebras, illustrating their broad relevance and interconnectedness.
Findings
Identifies multiple identities related to Ptolemy's theorem in cluster algebra contexts
Highlights the diverse applications of these identities across mathematical disciplines
Provides a conceptual overview of the 'zoo' of related identities
Abstract
In recent decades, identities similar to the one in the Ptolemy's theorem started to pop up in many fields in connection to the notion of cluster algebras introduced and studied since 2000 by Fomin and Zelevinsky. In this brief note we will try to describe several animals from this big and rich zoo. The note was written for the Association for Mathematical Research (AMR) "Reviews of Classic Results" series.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic