Categorical dynamical systems arising from sign-stable mutation loops
Category Theory
2021-05-19 v1 Algebraic Geometry
Dynamical Systems
Representation Theory
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].
Cite
@article{arxiv.2105.08332,
title = {Categorical dynamical systems arising from sign-stable mutation loops},
author = {Shunsuke Kano},
journal= {arXiv preprint arXiv:2105.08332},
year = {2021}
}
Comments
36 pages