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Deformations of the Lie–Poisson sphere of a compact semisimple Lie algebra
- Part of
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- Journal:
- Compositio Mathematica / Volume 150 / Issue 4 / April 2014
- Published online by Cambridge University Press:
- 27 March 2014, pp. 568-578
- Print publication:
- April 2014
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- Article
- Export citation
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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 equal than three around a degenerate (i.e. not symplectic) Poisson structure.
