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I-factorial quantum torsors and Heisenberg algebras of quantized enveloping type

Presented by: 
Kenny De Commer Vrije Universiteit Brussel
Tuesday 11th April 2017 - 14:00 to 15:00
INI Seminar Room 2
A I-factorial quantum torsor consists of an integrable, free and ergodic action of a locally compact quantum group on a type I-factor. We show how such actions admit a nice duality theory. As an example, we consider a deformed Heisenberg algebra associated to a quantum Borel algebra of a semisimple complex Lie algebra g. We show that, endowed with a *-structure swapping the two quantum Borel algebras inside, it allows a completion into a I-factorial quantum torsor for (an amplification of) the von Neumann algebraic completion of the compact form of the quantized enveloping algebra of g.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons