MIT Combinatorics Seminar
Cluster algebras of finite type and positive symmetrizable matrices
Andrei Zelevinsky
(Northeastern University, visiting MIT)
http://www.math.neu.edu/~zelevinsky/andrei.html
Wednesday, November 10, 2004
4:15 pm Room 2338
ABSTRACT

This is an account of a joint work with M.Barot and C.Geiss (UNAM, Mexico).
Although motivated by the theory of cluster algebras, the talk will be
purely combinatorial, so no knowledge of algebraic properties of
cluster algebras
(including their definition) will be assumed or needed. One should
just bear in mind an analogy between cluster algebras and KacMoody
algebras: both theories share the same classification of finite type
objects by familiar CartanKilling types. However the underlying
combinatorics beyond the two classifications is different: roughly
speaking, KacMoody algebras are associated with (symmetrizable)
Cartan matrices, while cluster algebras correspond to
skewsymmetrizable matrices. We discuss an interplay between the two
classes of matrices.
In particular, we establish a new criterion for deciding whether a
given skewsymmetrizable matrix gives rise to a cluster algebra of
finite type.


