caa a22 4500 469099119 CHVBK 20180323133040.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF00429998 doi (NATIONALLICENCE)springer-10.1007/BF00429998 Zakrzewski S. Institut für Theoretische Physik, TU Clausthal, Leibnizstr, 10, W-3392, Clausthal-Zellerfeld, Germany aut Poisson Lie groups and pentagonal transformations [Elektronische Daten] [S. Zakrzewski] Symplectic pentagonal transformations are intimately related to global versions of Poisson Lie groups (Manin groups, S *-groups, or symplectic pseudogroups). Symplectic pentagonal transformations of cotangent bundles, preserving the natural polarization, are shown to be in one to one correspondence with pentagonal transformations of the base manifold with a cocycle (if the base is connected and simply connected). By the results of Baaj and Skandalis, this allows to quantize (at the C *-algebra level!) those Poisson Lie groups, whose associated symplectic pentagonal transformation admits an invariant polarization. The (2n)2-parameter family of Poisson deformations of the (2n+1)-dimensional Heisenberg group described by Szymczak and Zakrzewski is shown to fall into this case. Kluwer Academic Publishers, 1992 Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 13-19 0377-9017 24:1<13 1992 24 11005 https://doi.org/10.1007/BF00429998 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00429998 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zakrzewski S. Institut für Theoretische Physik, TU Clausthal, Leibnizstr, 10, W-3392, Clausthal-Zellerfeld, Germany aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 13-19 0377-9017 24:1<13 1992 24 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer