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Deformations of the Lie–Poisson sphere of a compact semisimple Lie algebra
Abstract A compact semisimple Lie algebra $\mathfrak{g}$ induces a Poisson structure $\pi _{\mathbb{S}}$ on the unit sphere $\mathbb{S}(\mathfrak{g}^*)$ in $\mathfrak{g}^*$ . We compute the moduli space of Poisson structures on $\mathbb{S}(\mathfrak{g}^*)$ around $\pi _{\mathbb{S}}$ . This is the first explicit computation of a Poisson moduli space in dimension greater or …