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Inclusions of Von Neumann Algebras and Quantum Groupoı̈ds II

✍ Scribed by Michel Enock

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
604 KB
Volume
178
Category
Article
ISSN
0022-1236

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✦ Synopsis

In a previous article, in collaboration with Jean-Michel Vallin, we constructed two quantum groupo@ ds, dual to each other, from a depth 2 inclusion of von Neumann algebras M 0 /M 1 . In this paper we investigate this structure in greater detail. In the previous article, we constructed the analog of a co-product, while in this paper we define a co-inverse, by making the polar decomposition of the analog of the antipode, and left and right invariant Haar operator-valued weights. These two structures of quantum groupo@ ds, dual to each other, can be placed on the relative commutants M$ 0 & M 2 and M$ 1 & M 3 in such a way that the canonical Jones' tower associated to the inclusion can be described as a tower of successive crossed-products by these two structures.

📜 SIMILAR VOLUMES

Inclusions of von Neumann Algebras, and
Inclusions of von Neumann Algebras, and Quantum Groupoı̈ds
✍ Michel Enock; Jean-Michel Vallin 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 334 KB

From a depth 2 inclusion of von Neumann algebras M 0 /M 1 , with an operatorvalued weight verifying a regularity condition, we construct a pseudo-multiplicative unitary, which leads to two structures of Hopf bimodules, dual to each other. Moreover, we construct an action of one of these structures o