A (2n+1)-dimensional quantum group constructed from a skew-symmetric matrix

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Kahng, Byung-Jay

关键词: Poisson-Lie group;    Deformation quantization;    Locally compact quantum group;   

DOI  :  10.1016/j.geomphys.2011.06.010

来源: Elsevier

【 摘 要 】

Beginning with a skew-symmetric matrix, we define a certain Poisson-Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or Lie-Poisson) Poisson bracket. By analyzing this Poisson structure, we gather enough information to construct a C*-algebraic locally compact quantum group, via the cocycle bicrossed product construction method. The quantum group thus obtained is shown to be a deformation quantization of the Poisson-Lie group, in the sense of Rieffel. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free