Categorical dynamical systems arising from sign-stable mutation loops

Shunsuke Kano

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arXiv · 2105.08332

Categorical dynamical systems arising from sign-stable mutation loops

Shunsuke Kano

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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].

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Shunsuke Kano. 2021-05-18. Categorical dynamical systems arising from sign-stable mutation loops. https://arxiv.org/abs/2105.08332

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