Quantum cluster algebras
Quantum Algebra
2007-05-23 v2 Algebraic Geometry
Representation Theory
Abstract
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.
Cite
@article{arxiv.math/0404446,
title = {Quantum cluster algebras},
author = {Arkady Berenstein and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0404446},
year = {2007}
}
Comments
Minor corrections; final version, to appear in Advances in Mathematics; 41 pages