CLUSTER ALGEBRAS AND SEMIPOSITIVE SYMMETRIZABLE MATRICES


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Seven A. İ.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.363, ss.2733-2762, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 363
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1090/s0002-9947-2010-05255-9
  • Dergi Adı: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.2733-2762

Özet

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.