Cluster algebras in Lie and Knot theory
Mikhail Gorsky, Jos\'e Simental
TL;DR
This survey explores the connections between cluster algebras and link invariants, highlighting their roles in Lie theory and knot theory, and providing an overview of recent developments in these mathematical areas.
Contribution
It offers a comprehensive overview of how cluster algebras relate to Lie and knot theory, summarizing key concepts and recent research findings.
Findings
Cluster algebras provide a unifying framework for link invariants.
Connections between cluster algebras and Lie theory enhance understanding of knot invariants.
Recent developments reveal deep interactions between algebraic and topological structures.
Abstract
This is a survey article on some connections between cluster algebras and link invariants, written for the Notices of the AMS.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology