Abstract
We study finite-dimensional Lie algebras with given properties of subalgebras (like all proper subalgebras being abelian) and elements (like all elements being semisimple). We get results on both the structure of the whole class of algebras with the given property, and the structure of individual algebras in the class.
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Acknowledgments
This work was essentially done more than 20 years ago, while being a student at the Kazakh State University under the guidance of Askar Dzhumadil’daev, and has been reported at a few conferences in the Soviet Union at the end of 1980s. However, I find the results interesting and original enough even today to be put in writing, with some minor additions and modifications. During the final write-up I was supported by grants ERMOS7 (Estonian Science Foundation and Marie Curie Actions) and ETF9038 (Estonian Science Foundation).
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Zusmanovich, P. (2014). Lie Algebras with Given Properties of Subalgebras and Elements. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_7
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DOI: https://doi.org/10.1007/978-3-642-55361-5_7
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