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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

Cluster algebras I: Foundations


Authors: Sergey Fomin and Andrei Zelevinsky
Journal: J. Amer. Math. Soc. 15 (2002), 497-529
MSC (1991): Primary 14M99; Secondary 17B99
Published electronically: December 28, 2001
MathSciNet review: 1887642
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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.


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Additional Information

Sergey Fomin
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: fomin@umich.edu

Andrei Zelevinsky
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: andrei@neu.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-01-00385-X
PII: S 0894-0347(01)00385-X
Keywords: Cluster algebra, exchange pattern, Laurent phenomenon
Received by editor(s): April 13, 2001
Received by editor(s) in revised form: October 26, 2001
Published electronically: December 28, 2001
Additional Notes: The authors were supported in part by NSF grants #DMS-0049063, #DMS-0070685 (S.F.), and #DMS-9971362 (A.Z.)
Dedicated: To the memory of Sergei Kerov
Article copyright: © Copyright 2001 by Sergey Fomin and Andrei Zelevinsky