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Cluster algebras I: Foundations
Author(s):
Sergey
Fomin;
Andrei
Zelevinsky
Journal:
J. Amer. Math. Soc.
15
(2002),
497-529.
MSC (1991):
Primary 14M99;
Secondary 17B99
Posted:
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:
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
Posted:
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
Copyright of article:
Copyright
2001,
by Sergey Fomin and Andrei Zelevinsky
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