Categorical dynamical systems arising from sign-stable mutation loops

Abstract

We give an autoequivalence of the derived category of the Ginzburg dg algebra for a mutation loop satisfying the sign stability introduced in [IK21]. We compute the categorical entropies of their restrictions to some subcategories and conclude that they are both given by the logarithm of the cluster stretch factor. Moreover, we discuss the pseudo-Anosovness of them in the sense of [FFHKL19] and [DHKK14].

arXiv comment36 pages

References in corpus (15)

• Calabi-Yau algebras
• Flat surfaces and stability structures
• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
• A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines
• On entropy for autoequivalences of the derived category of curves
• On the categorical entropy and the topological entropy
• On Jacobian algebras from closed surfaces
• On Generalized Cluster Categories
• Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces
• $q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
• Curvature of the space of stability conditions
• Asymptotic shifting numbers in triangulated categories
• A characterization of pseudo-Anosov mapping classes via tropical cluster transformations
• Sign stability of mapping classes on marked surfaces II: general case via reductions