Matches in SemOpenAlex for { <https://semopenalex.org/work/W3105259938> ?p ?o ?g. }
- W3105259938 endingPage "108844" @default.
- W3105259938 startingPage "108844" @default.
- W3105259938 abstract "Consider a locally compact group G=Q⋉V such that V is abelian and the action of Q on the dual abelian group Vˆ has a free orbit of full measure. We show that such a group G can be quantized in three equivalent ways: by reflecting across the Galois object defined by the canonical irreducible representation of G on L2(V); by twisting the coproduct on the group von Neumann algebra of G by a dual 2-cocycle obtained from the G-equivariant Kohn–Nirenberg quantization of V×Vˆ; by considering the bicrossed product defined by a matched pair of subgroups of Q⋉Vˆ both isomorphic to Q. In the simplest case of the ax+b group over the reals, the dual cocycle in (2) is an analytic analogue of the Jordanian twist. It was first found by Stachura using different ideas. The equivalence of approaches (2) and (3) in this case implies that the quantum ax+b group of Baaj–Skandalis is isomorphic to the quantum group defined by Stachura. Along the way we prove a number of results for arbitrary locally compact groups G. Using recent results of De Commer we show that a class of G-Galois objects is parametrized by certain cohomology classes in H2(G;T). This extends results of Wassermann and Davydov in the finite group case. A new phenomenon is that already the unit class in H2(G;T) can correspond to a nontrivial Galois object. Specifically, we show that any nontrivial locally compact group G with group von Neumann algebra a factor of type I admits a canonical cohomology class of dual 2-cocycles such that the corresponding quantization of G is neither commutative nor cocommutative." @default.
- W3105259938 created "2020-11-23" @default.
- W3105259938 creator A5004643751 @default.
- W3105259938 creator A5008751492 @default.
- W3105259938 creator A5015605128 @default.
- W3105259938 creator A5065322831 @default.
- W3105259938 date "2021-02-01" @default.
- W3105259938 modified "2023-10-18" @default.
- W3105259938 title "Quantization of subgroups of the affine group" @default.
- W3105259938 cites W1541476201 @default.
- W3105259938 cites W1593975163 @default.
- W3105259938 cites W1963910623 @default.
- W3105259938 cites W1967677654 @default.
- W3105259938 cites W1973207973 @default.
- W3105259938 cites W1981479929 @default.
- W3105259938 cites W1986895732 @default.
- W3105259938 cites W1992287845 @default.
- W3105259938 cites W1996872878 @default.
- W3105259938 cites W1997453376 @default.
- W3105259938 cites W2003440110 @default.
- W3105259938 cites W2011039432 @default.
- W3105259938 cites W2027353566 @default.
- W3105259938 cites W2061388959 @default.
- W3105259938 cites W2081917558 @default.
- W3105259938 cites W2083474360 @default.
- W3105259938 cites W2085772114 @default.
- W3105259938 cites W2130795870 @default.
- W3105259938 cites W2227420806 @default.
- W3105259938 cites W2228987274 @default.
- W3105259938 cites W2262184227 @default.
- W3105259938 cites W2320712155 @default.
- W3105259938 cites W2950315040 @default.
- W3105259938 cites W2962705675 @default.
- W3105259938 cites W2963543948 @default.
- W3105259938 cites W2964018754 @default.
- W3105259938 cites W3100253556 @default.
- W3105259938 cites W3102371674 @default.
- W3105259938 cites W3105702455 @default.
- W3105259938 cites W3106230875 @default.
- W3105259938 cites W3128390254 @default.
- W3105259938 doi "https://doi.org/10.1016/j.jfa.2020.108844" @default.
- W3105259938 hasPublicationYear "2021" @default.
- W3105259938 type Work @default.
- W3105259938 sameAs 3105259938 @default.
- W3105259938 citedByCount "0" @default.
- W3105259938 crossrefType "journal-article" @default.
- W3105259938 hasAuthorship W3105259938A5004643751 @default.
- W3105259938 hasAuthorship W3105259938A5008751492 @default.
- W3105259938 hasAuthorship W3105259938A5015605128 @default.
- W3105259938 hasAuthorship W3105259938A5065322831 @default.
- W3105259938 hasBestOaLocation W31052599381 @default.
- W3105259938 hasConcept C116827671 @default.
- W3105259938 hasConcept C130133044 @default.
- W3105259938 hasConcept C136119220 @default.
- W3105259938 hasConcept C136170076 @default.
- W3105259938 hasConcept C142973675 @default.
- W3105259938 hasConcept C163572010 @default.
- W3105259938 hasConcept C178790620 @default.
- W3105259938 hasConcept C185592680 @default.
- W3105259938 hasConcept C187915474 @default.
- W3105259938 hasConcept C202444582 @default.
- W3105259938 hasConcept C20725272 @default.
- W3105259938 hasConcept C2776379255 @default.
- W3105259938 hasConcept C2781311116 @default.
- W3105259938 hasConcept C31498916 @default.
- W3105259938 hasConcept C33923547 @default.
- W3105259938 hasConcept C78606066 @default.
- W3105259938 hasConcept C81008192 @default.
- W3105259938 hasConceptScore W3105259938C116827671 @default.
- W3105259938 hasConceptScore W3105259938C130133044 @default.
- W3105259938 hasConceptScore W3105259938C136119220 @default.
- W3105259938 hasConceptScore W3105259938C136170076 @default.
- W3105259938 hasConceptScore W3105259938C142973675 @default.
- W3105259938 hasConceptScore W3105259938C163572010 @default.
- W3105259938 hasConceptScore W3105259938C178790620 @default.
- W3105259938 hasConceptScore W3105259938C185592680 @default.
- W3105259938 hasConceptScore W3105259938C187915474 @default.
- W3105259938 hasConceptScore W3105259938C202444582 @default.
- W3105259938 hasConceptScore W3105259938C20725272 @default.
- W3105259938 hasConceptScore W3105259938C2776379255 @default.
- W3105259938 hasConceptScore W3105259938C2781311116 @default.
- W3105259938 hasConceptScore W3105259938C31498916 @default.
- W3105259938 hasConceptScore W3105259938C33923547 @default.
- W3105259938 hasConceptScore W3105259938C78606066 @default.
- W3105259938 hasConceptScore W3105259938C81008192 @default.
- W3105259938 hasIssue "4" @default.
- W3105259938 hasLocation W31052599381 @default.
- W3105259938 hasLocation W31052599382 @default.
- W3105259938 hasLocation W31052599383 @default.
- W3105259938 hasOpenAccess W3105259938 @default.
- W3105259938 hasPrimaryLocation W31052599381 @default.
- W3105259938 hasRelatedWork W1034923237 @default.
- W3105259938 hasRelatedWork W1987778563 @default.
- W3105259938 hasRelatedWork W1993279369 @default.
- W3105259938 hasRelatedWork W210031726 @default.
- W3105259938 hasRelatedWork W2149347892 @default.
- W3105259938 hasRelatedWork W2318202296 @default.
- W3105259938 hasRelatedWork W3105259938 @default.