2017/02/27 by Kenny De Commer
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Crossed product #Mathematics #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Quantum spacetime #Realization (probability) #Type (biology) #math.OA #math.QA #math.RT
paper · pdf · doi:10.1016/j.jfa.2017.09.005
published as Journal of Functional Analysis 274 (1) (2018), 152-221 · 75 pages; the first four sections have appeared in the preprint arXiv:1612.00640, which will however not be published as such
arxiv created 2017/02/27 · openalex publication_date 2017/10/02 · arxiv updated 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.