Cluster algebras and semipositive symmetrizable matrices
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- by Ahmet I. Seven PDF
- Trans. Amer. Math. Soc. 363 (2011), 2733-2762 Request permission
Abstract:
There is a particular analogy between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices while Kac-Moody algebras correspond to (symmetrizable) generalized Cartan matrices. Both classes of algebras and the associated matrices have the same classification of finite type objects by the well-known Cartan-Killing types. In this paper, we study an extension of this correspondence to the affine type. In particular, we establish the cluster algebras which are determined by the generalized Cartan matrices of affine type.References
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Additional Information
- Ahmet I. Seven
- Affiliation: Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey
- MR Author ID: 764933
- Email: aseven@metu.edu.tr
- Received by editor(s): June 26, 2009
- Received by editor(s) in revised form: November 5, 2009, and November 18, 2009
- Published electronically: December 10, 2010
- Additional Notes: The author’s research was supported in part by the Scientific and Technological Research Council of Turkey (TUBITAK) grant #107T050
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 2733-2762
- MSC (2010): Primary 05E15; Secondary 13F60, 05C50, 15B36, 17B67
- DOI: https://doi.org/10.1090/S0002-9947-2010-05255-9
- MathSciNet review: 2763735