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

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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.



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