Amenability and vanishing of -Betti numbers: An operator algebraic approach

详细信息	查看全文 | 推荐本文 |

• 作者：Vadim Alekseev^a ; ^{alekseev@uni-math.gwdg.de} ; David Kyed^b ; ^{David.Kyed@wis.kuleuven.be}
• 关键词：Amenability ; L2-Betti numbers ; Operator algebras
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 August, 2012
• 卷：263
• 期：4
• 页码：1103-1128
• 文件大小：246 K

摘要

We introduce a F酶lner condition for dense subalgebras in finite von Neumann algebras and prove that it implies dimension flatness of the inclusion in question. It is furthermore proved that the F酶lner condition naturally generalizes the existing notions of amenability and that the ambient von Neumann algebra of a F酶lner algebra is automatically injective. As an application, we show how our techniques unify previously known results concerning vanishing of -Betti numbers for amenable groups, quantum groups and groupoids and moreover provide a large class of new examples of algebras with vanishing -Betti numbers.