ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

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説明

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.

収録刊行物

  • Osaka Journal of Mathematics

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

    Osaka University and Osaka Metropolitan University, Departments of Mathematics

詳細情報 詳細情報について

  • CRID
    1390015564796435456
  • NII書誌ID
    AA00765910
  • DOI
    10.18910/92413
  • HANDLE
    11094/92413
  • ISSN
    00306126
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • JaLC
    • IRDB

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