On the Approximate Periodicity of Sequences Attached to Non-Crystallographic Root Systems

ABSTRACT

We study Fomin–Zelevinsky's mutation rule in the context of non-crystallographic root systems. In particular, we construct approximately periodic sequences of real numbers for the non-crystallographic root systems of rank 2 by adjusting the exchange relation for cluster algebras. Moreover, we describe matrix mutation classes for types H₃ and H₄.

KEYWORDS:

• cluster algebra
• non-crystallographic root system
• approximate periodicity

2000 AMS Subject Classification:

• 13F60