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A remarkable contraction of semisimple Lie algebras

Dmitri I. Panyushev; Oksana S. Yakimova — 2012

Annales de l’institut Fourier

Recently, E.Feigin introduced a very interesting contraction $𝔮$ of a semisimple Lie algebra $𝔤$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of $𝔤$ . For instance, the algebras of invariants of both adjoint and coadjoint representations of $𝔮$ are free, and also the enveloping algebra of $𝔮$ is a free module over its centre.

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