Tubular Cluster Algebras II: Exponential growth

Abstract

Among the mutation finite cluster algebras the tubular ones are a particularly interesting class. We show that all tubular (simply laced) cluster algebras are of exponential growth by two different methods: first by studying the automorphism group of the corresponding cluster category and second by giving explicit sequences of mutations.

20 pages, v2: two typos on p. 13 fixed, v3: references to the related work by Felikson, Shapiro, Thomas and Tumarkin updated and extended. Final version, to appear in J. Pure Appl. Algebra

References in corpus (3)

• On triangulated orbit categories
• Cluster algebras and triangulated orbifolds
• On the c-vectors and g-vectors of the Markov cluster algebra

Cited by in corpus (5)

• On the c-vectors and g-vectors of the Markov cluster algebra
• Universal geometric coefficients for the once-punctured torus
• ${\tau }^2$-stable tilting complexes over weighted projective lines
• Tame algebras have dense $\mathbf{g}$-vector fans
• Acyclic cluster algebras with dense $g$-vector fans