On a class of finitary Lie algebras characterized through derivations
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- by Matej Brešar and Antonio Fernández López PDF
- Proc. Amer. Math. Soc. 138 (2010), 4161-4166 Request permission
Abstract:
Let $L$ be an infinite-dimensional simple Lie algebra over a field of characteristic $0$. Then there exist a derivation $d$ on $L$ and $n\ge 2$ such that $d^n$ is a nonzero finite rank map if and only if $L$ is finitary and contains a nonzero finite-dimensional abelian inner ideal. This is a partial statement of our main theorem. As auxiliary results needed for the proof we establish some properties of derivations in general nonassociative algebras.References
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Additional Information
- Matej Brešar
- Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadravska ulica 19, SI-1000 Ljubljana, Slovenia – and – Faculty of Natural Sciences and Mathematics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
- Email: matej.bresar@fmf.uni-lj.si
- Antonio Fernández López
- Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Malaga, Spain
- MR Author ID: 66255
- Email: emalfer@uma.es
- Received by editor(s): October 27, 2009
- Published electronically: August 10, 2010
- Additional Notes: The first author was supported by the Slovenian Research Agency (Program No. P1-0288).
The second author was supported by the MEC and Fondos FEDER, MTM2007-61978 - Communicated by: Gail R. Letzter
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 4161-4166
- MSC (2010): Primary 17B40, 17B65; Secondary 16W10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10644-5
- MathSciNet review: 2680042