{"_buckets": {"deposit": "bf0d0a78-d0ee-4bfd-973b-48e04d1e7692"}, "_deposit": {"created_by": 34, "id": "2000064", "owner": "34", "owners": [34], "owners_ext": {"displayname": "Fumie Nishikori", "username": "fumienishikori"}, "pid": {"revision_id": 0, "type": "depid", "value": "2000064"}, "status": "published"}, "_oai": {"id": "oai:oist.repo.nii.ac.jp:02000064", "sets": ["209"]}, "author_link": [], "control_number": "2000064", "item_10001_biblio_info_7": {"attribute_name": "Bibliographic Information", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2023-08-19", "bibliographicIssueDateType": "Issued"}, "bibliographic_titles": [{"bibliographic_title": "Journal of the London Mathematical Society", "bibliographic_titleLang": "en"}]}]}, "item_10001_creator_3": {"attribute_name": "Author", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Ariki Susumu", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "Lyle Sinéad", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "Speyer Liron", "creatorNameLang": "en"}]}]}, "item_10001_description_5": {"attribute_name": "Abstract", "attribute_value_mlt": [{"subitem_description": "For any algebra 𝐴 over an algebraically closed field 𝔽, we say that an 𝐴-module 𝑀 is Schurian ifEnd𝐴(𝑀) ≅ 𝔽. We say that 𝐴 is Schurian-finite if there are only finitely many isomorphism classes of Schurian 𝐴-modules, and Schurian-infinite otherwise. By work of Demonet, Iyama and Jasso, it is known that Schurian-finiteness is equivalent to 𝜏-tilting-finiteness, so thatwemay drawon a wealth of known results in the subject. We prove that for the type 𝐴 Hecke algebras with quantum characteristic 𝑒 ⩾ 3, all blocks of weight at least 2 are Schurianinfinite in any characteristic. Weight 0 and 1 blocks are known by results of Erdmann and Nakano to be representation finite, and are therefore Schurian-finite. This means that blocks oftype 𝐴 Hecke algebras (when 𝑒 ⩾ 3) are Schurian-infinite if and only if they have wild representation type if and only if the module category has finitely many wide subcategories. Along theway, we also prove a graded version of the Scopes equivalence, which is likely to be of independent interest.", "subitem_description_language": "en", "subitem_description_type": "Abstract"}]}, "item_10001_publisher_8": {"attribute_name": "Publisher", "attribute_value_mlt": [{"subitem_publisher": "London Mathematical Society", "subitem_publisher_language": "en"}, {"subitem_publisher": "Wiley", "subitem_publisher_language": "en"}]}, "item_10001_relation_10": {"attribute_name": "ISBN", "attribute_value_mlt": [{"subitem_relation_type_id": {"subitem_relation_type_id_text": "10.1112/jlms.12808", "subitem_relation_type_select": "DOI"}}]}, "item_10001_relation_14": {"attribute_name": "DOI", "attribute_value_mlt": [{"subitem_relation_type": "isIdenticalTo", "subitem_relation_type_id": {"subitem_relation_type_id_text": "10.1112/jlms.12808", "subitem_relation_type_select": "DOI"}}]}, "item_10001_relation_16": {"attribute_name": "情報源", "attribute_value_mlt": [{"subitem_relation_name": [{"subitem_relation_name_language": "en", "subitem_relation_name_text": "https://creativecommons.org/licenses/by/4.0/"}]}]}, "item_10001_relation_17": {"attribute_name": "Related site", "attribute_value_mlt": [{"subitem_relation_type": "isIdenticalTo", "subitem_relation_type_id": {"subitem_relation_type_id_text": "https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12808", "subitem_relation_type_select": "URI"}}]}, "item_10001_rights_15": {"attribute_name": "Rights", "attribute_value_mlt": [{"subitem_rights": "© 2023 The Authors.", "subitem_rights_language": "en"}]}, "item_10001_source_id_9": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0024-6107", "subitem_source_identifier_type": "PISSN"}, {"subitem_source_identifier": "1469-7750", "subitem_source_identifier_type": "EISSN"}]}, "item_10001_version_type_20": {"attribute_name": "Author\u0027s flag", "attribute_value_mlt": [{"subitem_version_resource": "http://purl.org/coar/version/c_970fb48d4fbd8a85", "subitem_version_type": "VoR"}]}, "item_access_right": {"attribute_name": "アクセス権", "attribute_value_mlt": [{"subitem_access_right": "open access", "subitem_access_right_uri": "http://purl.org/coar/access_right/c_abf2"}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_access", "date": [{"dateType": "Available", "dateValue": "2023-10-23"}], "download_preview_message": "", "file_order": 0, "filename": "Ariki-Schurian‐finiteness of blocks of type 𝑨 Hecke algebras.pdf", "filesize": [{"value": "3.8 MB"}], "future_date_message": "", "is_thumbnail": false, "licensetype": "license_0", "mimetype": "", "size": 3800000.0, "url": {"objectType": "fulltext", "url": "https://oist.repo.nii.ac.jp/record/2000064/files/Ariki-Schurian‐finiteness of blocks of type 𝑨 Hecke algebras.pdf"}, "version_id": "f92abcec-f86d-465d-a339-57da1ec18492"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Schurian‐finiteness of blocks of type 𝑨 Hecke algebras", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Schurian‐finiteness of blocks of type 𝑨 Hecke algebras", "subitem_title_language": "en"}]}, "item_type_id": "10001", "owner": "34", "path": ["209"], "permalink_uri": "https://oist.repo.nii.ac.jp/records/2000064", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2023-10-23"}, "publish_date": "2023-10-23", "publish_status": "0", "recid": "2000064", "relation": {}, "relation_version_is_last": true, "title": ["Schurian‐finiteness of blocks of type 𝑨 Hecke algebras"], "weko_shared_id": -1}
Schurian‐finiteness of blocks of type 𝑨 Hecke algebras
https://oist.repo.nii.ac.jp/records/2000064
https://oist.repo.nii.ac.jp/records/2000064