Quantization of the external algebra on a Poisson-Lie group

G. E. Arutyunov; P. B. Medvedev

Quantization of the external algebra on a Poisson-Lie group

High Energy Physics - Theory 2008-02-03 v2 Quantum Algebra

Authors: G. E. Arutyunov , P. B. Medvedev

Abstract

We show that the external algebra $\cal M$ on $GL(N)$ can be equipped with the graded Poisson brackets compatible with the group action. We prove that there are only two graded Poisson-Lie structures (brackets) on $\cal M$ and we obtain their explicit description. We realize that just these two structures appear as the quasiclassical limit of the bicovariant differential calculi on the quantum linear group $GL_q (N)$ .

Keywords

external algebra Poisson-Lie group graded Poisson brackets quantum group bicovariant differential calculus quasiclassical limit

Cite

@article{arxiv.hep-th/9311096,
  title  = {Quantization of the external algebra on a Poisson-Lie group},
  author = {G. E. Arutyunov and P. B. Medvedev},
  journal= {arXiv preprint arXiv:hep-th/9311096},
  year   = {2008}
}

Comments

19 pages. The proof of eq.(3.16) and LaTeX errors are corrected

Quantization of the external algebra on a Poisson-Lie group

Abstract

Keywords

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