Surprising properties of centralisers in classical Lie algebras
Oksana Yakimova (2009)
Annales de l’institut Fourier
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Let be a classical Lie algebra, , either , , or and let be a nilpotent element of . We study various properties of the centralisers . The first four sections deal with rather elementary questions, like the centre of , commuting varieties associated with , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on and symmetric invariants of .