%0 Journal Article
%T A remarkable contraction of semisimple Lie algebras
%A Dmitri Panyushev
%A Oksana Yakimova
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1107.0702v1