ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

Barbacovi, Federico; Kim, Jongmyeong

doi:https://doi.org/10.18910/92413

ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

Barbacovi, Federico; Kim, Jongmyeong

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

アクセス数:110件（2026-07-27 03:03 集計）

固定URL: https://doi.org/10.18910/92413

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タイトル	ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS
著者	著者名 Barbacovi, Federico
著者	著者名 Kim, Jongmyeong
抄録	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.
出版者	Osaka University and Osaka Metropolitan University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	60(3)
ページ	653-670
刊行年月	2023-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/92413
DOI	https://doi.org/10.18910/92413
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 60, Number 3 （2023-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2023, 60(3), p. 653-670
DC.title	ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS
DC.creator	Barbacovi, Federico
DC.creator	Kim, Jongmyeong
DC.publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2023-07
DCTERMS.abstract	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.
DC.identifier	10.18910/92413
DC.format	92413
citation_title	ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS
citation_author	Barbacovi, Federico
citation_author	Kim, Jongmyeong
citation_publisher	Osaka University and Osaka Metropolitan University, Departments of Mathematics
citation_language	英語
citation_date	2023-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	60
citation_issue	3
citation_firstpage	653
citation_lastpage	670
citation_public_url	https://hdl.handle.net/11094/92413
citation_doi_detail	10.18910/92413
citation_doi	https://doi.org/10.18910/92413

ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

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