Crossed products by groupoid actions and their smooth flows of weights
type: Item
instance of: scholarly article
title: Crossed products by groupoid actions and their smooth flows of weights
zbMATH Open document ID: 0824.46080
author: Takehiko Yamanouchi
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1995-11-13T00:00:00Z
review text: In [`Duality for actions and coactions of measured proupoids on vonNeumann algebras', Mem. Am. Math. Soc. 484, 101 p. (1993; Zbl 0822.46070)], the author introduced the notion of an action and a coaction of a measurable groupoid on a von Neumann algebra. He constructed their crossed product, dual (co)action and extended the Nakagami-Takesaki duality theorem. In the present paper the crossed product is realized as the left von Neumann algebra of a left Hilbert algebra. This generalizes known results for the group action to the groupoid setting.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 597455
zbMATH Keywords: groupoid action
zbMATH Keywords: action
zbMATH Keywords: coaction of a measurable groupoid on a von Neumann algebra
zbMATH Keywords: crossed product
zbMATH Keywords: Nakagami-Takesaki duality theorem
zbMATH Keywords: left von Neumann algebra of a left Hilbert algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195168206
OpenAlex ID: W2036963235
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DOI: 10.2977/PRIMS/1195168206
description: scientific article; zbMATH DE number 597455