Serial subalgebras of finitary Lie algebras
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- by Felix Leinen and Orazio Puglisi PDF
- Proc. Amer. Math. Soc. 129 (2001), 45-51 Request permission
Abstract:
A Lie subalgebra $L$ of ${\mathfrak {gl}_{{\mathbb {K}}}(V)}$ is said to be finitary if it consists of elements of finite rank. We show that, if $L$ acts irreducibly on $V$, and if $V$ is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of $L$ acts irreducibly on $V$ too. When $\operatorname {Char} \mathbb {K}\neq 2$, it follows that the locally solvable radical of such $L$ is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic $\neq 2$ are hyperabelian.References
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Additional Information
- Felix Leinen
- Affiliation: Fachbereich 17 – Mathematik, Johannes Gutenberg–Universität Mainz, D–55099 Mainz, Germany
- Address at time of publication: Department of Mathematics, University of Newcastle, Newcastle upon Tyne NE1 7RU, United Kingdom
- Email: Leinen@mathematik.uni-mainz.de, F.A.Leinen@ncl.ac.uk
- Orazio Puglisi
- Affiliation: Dipartimento di Matematica, Università degli Studi di Trento, I–38050 Povo (Trento), Italy
- Email: puglisi@alpha.science.unitn.it
- Received by editor(s): September 3, 1998
- Received by editor(s) in revised form: March 22, 1999
- Published electronically: July 27, 2000
- Communicated by: Roe Goodman
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 45-51
- MSC (1991): Primary 17B65, 17B50
- DOI: https://doi.org/10.1090/S0002-9939-00-05496-4
- MathSciNet review: 1694350