CLUSTER ALGEBRAS AND CLUSTER CATEGORIES

Document Type : Other

Author

Abstract

These are notes from introductory survey lectures given
at the Institute for Studies in Theoretical Physics and Mathematics
(IPM), Teheran, in 2008 and 2010. We present the definition and
the fundamental properties of Fomin-Zelevinsky’s cluster algebras.
Then, we introduce quiver representations and show how they can
be used to construct cluster variables, which are the canonical generators
of cluster algebras. From quiver representations, we proceed
to the cluster category, which yields a complete categorification of
the cluster algebra and its combinatorial underpinnings.

Keywords


Volume 37, No. 2
Proceedings of the 8th Seminar of Dierential Equations, Dynamical Systems and their Applications
July 2011
Pages 187-234
  • Receive Date: 09 February 2011
  • Revise Date: 19 April 2011
  • Accept Date: 20 April 2011