Irreducible inclusions of factors, multiplicative unitaries, and Kac algebras
type: Item
instance of: scholarly article
title: Irreducible inclusions of factors, multiplicative unitaries, and Kac algebras
zbMATH Open document ID: 0847.22003
author: Michel Enock
author: Ryszard Nest
published in: Journal of Functional Analysis
publication date: 1996-06-30T00:00:00Z
review text: From an irreducible depth 2 inclusion of factors, verifying a regularity condition, the authors construct a multiplicative unitary, and an action, at every level of the canonical tower constructed from the inclusion; when this inclusion admits a faithful semifinite normal operator-valued weight, stronger conditions are given, and the tower appears then as a crossed-product construction. In particular they rederive Herman and Ocneanu's results when the inclusion admits a faithful normal conditional expectation, and the tower is then the crossed-product construction, alternatively by a compact quantum group and by its dual, and, more precisely, according to Yamagami's result, by a compact type Kac algebra and by its dual.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 22D12
Mathematics Subject Classification ID: 22D25
zbMATH DE Number: 880571
zbMATH Keywords: group-like structure
zbMATH Keywords: multiplicative unitaries
zbMATH Keywords: irreducible depth 2 inclusion
zbMATH Keywords: canonical tower
zbMATH Keywords: operator-valued weight
zbMATH Keywords: faithful normal conditional expectation
zbMATH Keywords: compact quantum group
zbMATH Keywords: Kac algebra
MaRDI profile type: Publication
full work available at URL: jfan.1996.0053
OpenAlex ID: W2061634703
DOI: 10.1006/JFAN.1996.0053
description: scientific article; zbMATH DE number 880571