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.
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}
}