A remarkable contraction of semisimple Lie algebras
Annales de l'Institut Fourier, Volume 62 (2012) no. 6, p. 2053-2068

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.

E. Feigin a introduit la contraction 𝔮 d’une algèbre de Lie semi-simple 𝔤 dans arXiv :1007.0646 et arXiv :1101.1898. Nous démontrons que ces algèbres de Lie non-réductives conservent quelque unes des propriétés de 𝔤. En particulier, les algèbres des invariants des représentations adjointe et respectivement coadjointe de 𝔮 sont libres, et l’algèbre enveloppante de 𝔮 est un module libre sur son centre.

DOI : https://doi.org/10.5802/aif.2742
Classification:  13A50,  14L30,  17B40,  22E46
Keywords: Inönü-Wigner contraction, coadjoint representation, algebra of invariants, orbit
@article{AIF_2012__62_6_2053_0,
     author = {Panyushev, Dmitri I. and Yakimova, Oksana S.},
     title = {A remarkable contraction of semisimple Lie algebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {6},
     year = {2012},
     pages = {2053-2068},
     doi = {10.5802/aif.2742},
     mrnumber = {3060751},
     zbl = {1266.13003},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_6_2053_0}
}
Panyushev, Dmitri I.; Yakimova, Oksana S. A remarkable contraction of semisimple Lie algebras. Annales de l'Institut Fourier, Volume 62 (2012) no. 6, pp. 2053-2068. doi : 10.5802/aif.2742. http://www.numdam.org/item/AIF_2012__62_6_2053_0/

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