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Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

Paul Sherman·Andrei Zelevinsky
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Abstract

The main motivation for the study of cluster algebras initiated in math.RT/0104151, math.RA/0208229 and math.RT/0305434 was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic groups. In this paper, we introduce and explicitly construct the canonical basis for a special family of cluster algebras of rank 2.

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Paul Sherman, Andrei Zelevinsky. 2003-12-15. Positivity and canonical bases in rank 2 cluster algebras of finite and affine types. https://arxiv.org/abs/math/0307082

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