English

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

Operator Algebras 2015-05-28 v1 Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.1106.1920,
  title  = {A (2n+1)-dimensional quantum group constructed from a skew-symmetric matrix},
  author = {Byung-Jay Kahng},
  journal= {arXiv preprint arXiv:1106.1920},
  year   = {2015}
}
R2 v1 2026-06-21T18:20:15.540Z