TL;DR
This paper introduces (upper) cluster algebras, explores their bases through topological models, discusses tropical properties, and relates these concepts to representation theory, providing insights into their structure and quantization.
Contribution
It presents new families of bases for (upper) cluster algebras using topological models and discusses their tropical and representation-theoretic properties.
Findings
Introduction of several important bases for cluster algebras
Analysis of tropical properties of these bases
Connection between bases and representation theory
Abstract
We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these bases and their relation to representation theory. This article is an extended version of the talk given at the 19th International Conference on Representations of Algebras (ICRA 2020).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics