Quantization of the external algebra on a Poisson-Lie group

Abstract

We show that the external algebra $\mathcal{M}$ 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 $\mathcal{M}$ 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 $G{L}_q(N)$.

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