ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

Barbacovi Federico, Kim Jongmyeong

doi:10.18910/92413

Description

Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of two endofunctors is hard, and in general the result doesn’t have to be related to the entropy of the single pieces. In this paper we compute the entropy of the composition of two spherical twists around spherical objects, showing that it depends on the dimension of the graded vector space of morphisms between them. As a consequence of these computations we produce new counterexamples to Kikuta–Takahashi’s conjecture. In particular, we describe the first counterexamples in odd dimension and examples for the d-Calabi–Yau Ginzburg dg algebra associated to the A₂ quiver.

Journal

Osaka Journal of Mathematics

Osaka Journal of Mathematics 60 (3), 653-670, 2023-07

Osaka University and Osaka Metropolitan University, Departments of Mathematics

Details 詳細情報について

CRID: 1390015564796435456

NII Book ID: AA00765910

DOI: 10.18910/92413

HANDLE: 11094/92413

ISSN: 00306126

Text Lang: en

Article Type: departmental bulletin paper

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