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2021-03-06
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このアイテムへのリンクには次のURLをご利用ください:
https://doi.org/10.18910/76681
このアイテムへのリンクには次のURLをご利用ください:http://hdl.handle.net/11094/76681
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論文情報
タイトル
MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS
著者
Schaps, Mary
Schaps, Mary
Zvi, Zehavit
Zvi, Zehavit
抄録
Brauer tree algebras are important and fundamental blocks in the representation theory of finite dimensional algebras. In this research, we present a combination of two main approaches to the tilting theory of Brauer tree algebras. The first approach is the theory initiated by Rickard, providing a direct link between an ordinary Brauer tree algebra and the Brauer star algebra. This approach was continued by Schaps-Zakay with their theory of pointing the tree. The second approach is the theory developed by Aihara, relating to the sequence of mutations from the ordinary Brauer tree algebra to the Brauer star algebra. Our main purpose in this research is to combine these two approaches. We first find an algorithm based on centers which are all terminal edges, for which we are able to obtain a tilting complex constructed from irreducible complexes of length two [13], which is obtained from a sequence of mutations. In [1], Aihara gave an algorithm for reducing from tree to star by mutations and showed that it gave a two-term tree-to-star complex. We prove that Aihara’s complex is obtained from the corresponding completely folded Rickard tree-to-star complex by a permutation of projectives.
公開者
Osaka University and Osaka City University, Departments of Mathematics
掲載誌名
Osaka Journal of Mathematics
巻
57
号
3
開始ページ
689
終了ページ
709
刊行年月
2020-07
ISSN
00306126
NCID
AA00765910
URL
http://hdl.handle.net/11094/76681
言語
英語
DOI
info:doi/10.18910/76681
カテゴリ
紀要論文 Departmental Bulletin Paper
Osaka Journal of Mathematics / Volume 57, Number 3 （2020-7）
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DCTERMS.bibliographicCitation
Osaka Journal of Mathematics.57(3) P.689-P.709
DC.title
MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS
DC.creator
Schaps, Mary
Zvi, Zehavit
DC.publisher
Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766
英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF
2020-07
DC.identifier" scheme="DCTERMS.URI
http://hdl.handle.net/11094/76681
DCTERMS.abstract
Brauer tree algebras are important and fundamental blocks in the representation theory of finite dimensional algebras. In this research, we present a combination of two main approaches to the tilting theory of Brauer tree algebras. The first approach is the theory initiated by Rickard, providing a direct link between an ordinary Brauer tree algebra and the Brauer star algebra. This approach was continued by Schaps-Zakay with their theory of pointing the tree. The second approach is the theory developed by Aihara, relating to the sequence of mutations from the ordinary Brauer tree algebra to the Brauer star algebra. Our main purpose in this research is to combine these two approaches. We first find an algorithm based on centers which are all terminal edges, for which we are able to obtain a tilting complex constructed from irreducible complexes of length two [13], which is obtained from a sequence of mutations. In [1], Aihara gave an algorithm for reducing from tree to star by mutations and showed that it gave a two-term tree-to-star complex. We prove that Aihara’s complex is obtained from the corresponding completely folded Rickard tree-to-star complex by a permutation of projectives.
DC.identifier
info:doi/10.18910/76681
citation_title
MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS
citation_author
Schaps, Mary
Zvi, Zehavit
citation_publisher
Osaka University and Osaka City University, Departments of Mathematics
citation_language
英語
citation_date
2020-07
citation_journal_title
Osaka Journal of Mathematics
citation_volume
57
citation_issue
3
citation_firstpage
689
citation_lastpage
709
citation_issn
00306126
citation_public_url
http://hdl.handle.net/11094/76681
citation_doi
info:doi/10.18910/76681