Minimal Mutation-Infinite Quivers

ABSTRACT

Quivers constructed from hyperbolic Coxeter simplices give examples of minimal mutation-infinite quivers; however, they are not the only such quivers. We classify minimal mutation-infinite quivers through a number of moves and link the representatives of the classes with the hyperbolic Coxeter simplices, plus exceptional classes which are not related to simplices.

KEYWORDS:

• cluster algebra
• Coxeter diagram
• quiver mutation

2000 AMS SUBJECT CLASSIFICATION:

• 13F60 (primary)
• 20F55 (secondary)

Acknowledgments

The author would like to thank John Parker and Pavel Tumarkin for their supervision and support.

Funding

The author’s PhD studies are supported by an EPSRC studentship.