Quantum cluster algebras

Details Quantum cluster algebras Quantum cluster algebras

2004-04-24

arxiv.org/abs/math/0404446v2

Mathematics

Quantum Algebra

Minor corrections; final version, to appear in Advances in Mathematics; 41 pages

Scientific paper

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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