Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Cluster algebras and semipositive symmetrizable matrices

Author: Ahmet I. Seven
Journal: Trans. Amer. Math. Soc. 363 (2011), 2733-2762
MSC (2010): Primary 05E15; Secondary 13F60, 05C50, 15B36, 17B67
Published electronically: December 10, 2010
MathSciNet review: 2763735
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 05E15, 13F60, 05C50, 15B36, 17B67

Retrieve articles in all journals with MSC (2010): 05E15, 13F60, 05C50, 15B36, 17B67

Additional Information

Ahmet I. Seven
Affiliation: Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

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
Article copyright: © Copyright 2010 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia