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arXiv · 1702.08191

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

Kenny De Commer
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Abstract

We introduce a notion of I-factorial quantum torsor, which consists of an integrable ergodic action of a locally compact quantum group on a type I-factor such that also the crossed product is a type I-factor. We show that any such I-factorial quantum torsor is at the same time a I-factorial quantum torsor for the dual locally compact quantum group, in such a way that the construction is involutive. As a motivating example, we show that quantized compact semisimple Lie groups, when amplified via a crossed product construction with the function algebra on the associated weight lattice, admit I-factorial quantum torsors, and give an explicit realization of the dual quantum torsor in terms of a deformed Heisenberg algebra for the Borel part of a quantized universal enveloping algebra.

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Kenny De Commer. 2017-02-27. I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type. https://doi.org/10.1016/j.jfa.2017.09.005

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