A remarkable contraction of semisimple Lie algebras

Dmitri I. Panyushev[1]; Oksana S. Yakimova[2]

  • [1] Institute for Information Transmission Problems of the R.A.S. B. Karetnyi per. 19 Moscow 127994 (Russia)
  • [2] Friedrich-Schiller-Universität Jena Mathematisches Institut Jena D-07737 (Deutschland)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 6, page 2053-2068
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Panyushev, Dmitri I., and Yakimova, Oksana S.. "A remarkable contraction of semisimple Lie algebras." Annales de l’institut Fourier 62.6 (2012): 2053-2068. <http://eudml.org/doc/251140>.

@article{Panyushev2012,
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.},
affiliation = {Institute for Information Transmission Problems of the R.A.S. B. Karetnyi per. 19 Moscow 127994 (Russia); Friedrich-Schiller-Universität Jena Mathematisches Institut Jena D-07737 (Deutschland)},
author = {Panyushev, Dmitri I., Yakimova, Oksana S.},
journal = {Annales de l’institut Fourier},
keywords = {Inönü-Wigner contraction; coadjoint representation; algebra of invariants; orbit; Inonu-Wigner contraction; invariant algebras; adjoint representation},
language = {eng},
number = {6},
pages = {2053-2068},
publisher = {Association des Annales de l’institut Fourier},
title = {A remarkable contraction of semisimple Lie algebras},
url = {http://eudml.org/doc/251140},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Panyushev, Dmitri I.
AU - Yakimova, Oksana S.
TI - A remarkable contraction of semisimple Lie algebras
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 6
SP - 2053
EP - 2068
AB - 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.
LA - eng
KW - Inönü-Wigner contraction; coadjoint representation; algebra of invariants; orbit; Inonu-Wigner contraction; invariant algebras; adjoint representation
UR - http://eudml.org/doc/251140
ER -

References

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