Cluster algebras I: Foundations-Reference-Cited by-同舟云学术

Cluster algebras I: Foundations

Published:2001-12-28 Issue:2 Volume:15 Page:497-529
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Fomin Sergey,Zelevinsky Andrei

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2002-15-02/S0894-0347-01-00385-X/S0894-0347-01-00385-X.pdf

Reference20 articles.

1. Parametrizations of canonical bases and totally positive matrices;Berenstein, Arkady;Adv. Math.,1996

2. String bases for quantum groups of type 𝐴ᵣ;Berenstein, Arkady,1993

3. Total positivity in Schubert varieties;Berenstein, Arkady;Comment. Math. Helv.,1997

4. bz01 A. Berenstein and A. Zelevinsky, Tensor product multiplicities, canonical bases and totally positive varieties, \textsl{Invent. Math.} 143 (2001), 77–128.

5. Double Bruhat cells and total positivity;Fomin, Sergey;J. Amer. Math. Soc.,1999

Cited by 1112 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Cluster characters for 2-Calabi-Yau Frobenius extriangulated categories;Journal of Algebra;2024-12

2. Some properties of generalized cluster algebras of geometric type;Journal of Algebra;2024-12

3. Chromatic numbers for facet colouring of some generalised associahedra;Discrete Applied Mathematics;2024-12

4. A positive/tropical critical point theorem and mirror symmetry;Advances in Mathematics;2024-11

5. Cluster realisations of ıquantum$\imath {\rm quantum}$ groups of type AI;Proceedings of the London Mathematical Society;2024-09-12