I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type |
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Authors: | Kenny De Commer |
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Affiliation: | Vakgroep wiskunde, Vrije Universiteit Brussel (VUB), B-1050 Brussels, Belgium |
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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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Keywords: | Locally compact quantum groups Quantized enveloping algebras Galois objects |
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