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arxiv: math/0404446 · v2 · submitted 2004-04-24 · 🧮 math.QA · math.AG· math.RT

Quantum cluster algebras

Arkady Berenstein , Andrei Zelevinsky This is my paper
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keywords algebrasclustermathquantumalgebraicanalogsbasescanonical
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Cluster algebras were introduced by S. Fomin and A. Zelevinsky in math.RT/0104151; their study continued in math.RA/0208229, math.RT/0305434. This is a family of commutative rings designed to serve as an algebraic framework for the theory of total positivity and canonical bases in semisimple groups and their quantum analogs. In this paper we introduce and study quantum deformations of cluster algebras.

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