ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING

Miyamoto, Kengo

doi:https://doi.org/10.18910/73353

ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING

Miyamoto, Kengo

Osaka Journal of Mathematics, 2019, 56(3), 459-496

アクセス数:116件（2025-03-12 13:28 集計）

固定URL: https://doi.org/10.18910/73353

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タイトル	ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING
著者	著者名 Miyamoto, Kengo
抄録	We consider the Kronecker algebra 𝐴= ϑ[𝑋, 𝑌]/(𝑋², 𝑌²), where ϑ is a complete discrete valuation ring. Since 𝐴 ⨂ κ is a special biserial algebra, where κ is the residue field of ϑ, one can compute a complete list of indecomposable 𝐴 ⨂ κ-modules. For each indecomposable 𝐴 ⨂ κ-module, we obtain a special kind of -lattices called “Heller lattices”. In this paper, we determine the non-periodic component of a variant of the stable Auslander–Reiten quiver fo the category of 𝐴-lattices that contains “Heller lattices”.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	56(3)
ページ	459-496
刊行年月	2019-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73353
DOI	https://doi.org/10.18910/73353
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 56, Number 3 （2019-7）

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. 2019, 56(3), p. 459-496
DC.title	ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING
DC.creator	Miyamoto, Kengo
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2019-07
DCTERMS.abstract	We consider the Kronecker algebra 𝐴= ϑ[𝑋, 𝑌]/(𝑋², 𝑌²), where ϑ is a complete discrete valuation ring. Since 𝐴 ⨂ κ is a special biserial algebra, where κ is the residue field of ϑ, one can compute a complete list of indecomposable 𝐴 ⨂ κ-modules. For each indecomposable 𝐴 ⨂ κ-module, we obtain a special kind of -lattices called “Heller lattices”. In this paper, we determine the non-periodic component of a variant of the stable Auslander–Reiten quiver fo the category of 𝐴-lattices that contains “Heller lattices”.
DC.identifier	10.18910/73353
DC.format	73353
citation_title	ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING
citation_author	Miyamoto, Kengo
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2019-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	56
citation_issue	3
citation_firstpage	459
citation_lastpage	496
citation_public_url	https://hdl.handle.net/11094/73353
citation_doi_detail	10.18910/73353
citation_doi	https://doi.org/10.18910/73353

ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING

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