Study of quantum group actions on von Neumann algebras

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740095
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Hokkaido University
• Principal Investigator: TOMATSU Reiji 北海道大学, 理学(系)研究科(研究院), 准教授 (70447366)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 作用素環 / von Neumann環 / C*環 / 量子群

Outline of Final Research Achievements

My main research results are ``Analysis of infinite tensor product type actions",``Formulation of Haagerup approximation property for arbitrary von Neumann algebras" and ``Study of Haagerup approximation property of von Neumann algebra by bimodule approach". I showed that any infinite tensor product type action of a q-deformed quantum group is actually induced from its maximal torus. I formulated Haagerup approximation property by using theory of completely positive operators on standard Hilbert spaces of von Neumann algebras. By bimodule approach, I succeeded in strengthening some results obtained before.

Free Research Field

作用素環論