Harmonic cocycles and von Neumann algebras

来源 :算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni | 被引量 : 0次 | 上传用户：hqchunyun

【摘要】

：

　　Important classes of locally compact groups(such as groups with Kazhdans property and groups with the Haagerup property)are characterized by their actions b

【作者】

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Bachir Bekka

【机构】

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IRMAR,UMR-CNRS6625UniversitédeRennes1,CampusBeaulieu,F-35042RennesCedex,France

【出处】

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算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni

【发表日期】

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2017年12期

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　　Important classes of locally compact groups(such as groups with Kazhdans property and groups with the Haagerup property)are characterized by their actions by affine isometries on Hilbert spaces.Such an action is described by a space of 1-cohomology with coefficients in a unitary group representation.Using harmonic cocycles,the space of(reduced)1-cohomology can be turned into a Hilbert module over the von Neumann algebra given by the commutant of the representation.We will be interested in the associated von Neumann dimension in the case of a factor representation and its relation to a notion of irreducibility for actions by affine isometries.

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