Quantization of the external algebra on a Poisson-Lie group

G. E. Arutyunov; P. B. Medvedev

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arXiv · hep-th/9311096

Quantization of the external algebra on a Poisson-Lie group

G. E. Arutyunov·P. B. Medvedev

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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 $GL_q (N)$.

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G. E. Arutyunov, P. B. Medvedev. 1994-02-04. Quantization of the external algebra on a Poisson-Lie group. https://arxiv.org/abs/hep-th/9311096

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