MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS

Schaps, Mary; Zvi, Zehavit

doi:info:doi/10.18910/76681

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タイトル	MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS
著者	Schaps, Mary Schaps, Mary
著者	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
カテゴリ	Osaka Journal of Mathematics / Volume 57, Number 3 （2020-7）

著者版フラグ	publisher
NII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.57(3) P.689-P.709
DC.title	MUTATIONS AND POINTING FOR BRAUER TREE ALGEBRAS
DC.creator	Schaps, Mary
DC.creator	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
citation_author	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

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