## Cluster algebras I: Foundations

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Sergey Fomin and Andrei Zelevinsky
**HTML**| PDF - J. Amer. Math. Soc.
**15**(2002), 497-529

## 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.## References

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*Adv. in Applied Math.*

## Additional Information

**Sergey Fomin**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 230455
- ORCID: 0000-0002-4714-6141
- Email: fomin@umich.edu
**Andrei Zelevinsky**- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- Email: andrei@neu.edu
- 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.)
- © Copyright 2001 by Sergey Fomin and Andrei Zelevinsky
- Journal: J. Amer. Math. Soc.
**15**(2002), 497-529 - MSC (1991): Primary 14M99; Secondary 17B99
- DOI: https://doi.org/10.1090/S0894-0347-01-00385-X
- MathSciNet review: 1887642

Dedicated: To the memory of Sergei Kerov