Cluster algebras I: Foundations
Sergey Fomin, Andrei Zelevinsky
TL;DR
This paper introduces the foundational theory of cluster algebras, a new class of commutative algebras aimed at advancing the understanding of dual canonical bases and total positivity in semisimple groups.
Contribution
It establishes the initial framework and fundamental properties of cluster algebras, providing a basis for further research in algebraic and geometric applications.
Findings
Defined the structure of cluster algebras
Connected cluster algebras to dual canonical bases
Laid groundwork for total positivity studies
Abstract
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons