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

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• Kenny De Commer (Vrije Universiteit Brussel)
• Tuesday 11 April 2017, 14:00-15:00
• Seminar Room 2, Newton Institute.

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OAS - Operator algebras: subfactors and their applications

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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