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arXiv · 1107.0702

A remarkable contraction of semisimple Lie algebras

Dmitri Panyushev·Oksana Yakimova
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Abstract

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

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Dmitri Panyushev, Oksana Yakimova. 2011-07-04. A remarkable contraction of semisimple Lie algebras. https://arxiv.org/abs/1107.0702

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