Computing Cluster Expansions via matrices

Emine Yildirim (University of Leeds)

Wednesday 8th March, 2023 16:00-17:00 Maths 311B


Cluster algebras are commutative rings which are defined recursively from a set of initial set of generators, and one writes all the other generators in terms of the initial ones. There are different ways to get expansion formulas for the generators (simply called cluster expansions). For instance, we may use the combinatorics of snake graphs, T-paths or so-called CC-map in the representation theory of algebras. In a joint work with E. Kantarcı OÄŸuz, we compute the cluster expansion formulas using 2 by 2 matrices for the cluster algebra elements associated with arcs coming from surfaces. The method we introduce is quite efficient and can be generalised to different settings.

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