A GROUPOID APPROACH TO LÜCK’S AMENABILITY CONJECTURE

Kyed, David; D. Petersen, Henrik

Osaka Journal of Mathematics, 2014, 51(4), 905-934

アクセス数:259件（2026-04-05 23:42 集計）

固定URL: https://doi.org/10.18910/50980

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タイトル	A GROUPOID APPROACH TO LÜCK’S AMENABILITY CONJECTURE
著者	著者名 Kyed, David
著者	著者名 D. Petersen, Henrik
抄録	We prove that amenability of a discrete group is equivalent to dimension flatness of certain ring inclusions naturally associated with measure preserving actions of the group. This provides a group-measure space theoretic solution to a conjecture of Lück stating that amenability of a group is characterized by dimension flatness of the inclusion of its complex group algebra into the associated von Neumann algebra.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	51(4)
ページ	905-934
刊行年月	2014-10
言語	英語
ハンドルURL	https://hdl.handle.net/11094/50980
DOI	https://doi.org/10.18910/50980
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 51, Number 4　(2014-10）

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. 2014, 51(4), p. 905-934
DC.title	A GROUPOID APPROACH TO LÜCK’S AMENABILITY CONJECTURE
DC.creator	Kyed, David
DC.creator	D. Petersen, Henrik
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	2014-10
DCTERMS.abstract	We prove that amenability of a discrete group is equivalent to dimension flatness of certain ring inclusions naturally associated with measure preserving actions of the group. This provides a group-measure space theoretic solution to a conjecture of Lück stating that amenability of a group is characterized by dimension flatness of the inclusion of its complex group algebra into the associated von Neumann algebra.
DC.identifier	10.18910/50980
DC.format	50980
citation_title	A GROUPOID APPROACH TO LÜCK’S AMENABILITY CONJECTURE
citation_author	Kyed, David
citation_author	D. Petersen, Henrik
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	4
citation_firstpage	905
citation_lastpage	934
citation_public_url	https://hdl.handle.net/11094/50980
citation_doi_detail	10.18910/50980
citation_doi	https://doi.org/10.18910/50980