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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 2, Pages 35–44 (Mi ivm8972)  
On the maximal finite-dimensional Lie algebras with given nilradical

V. V. Gorbatsevich

Chair of Higher Mathematics, Russian State Technological University, 3 Orshanskaya str., Moscow, 121552 Russia
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Abstract: We study the set of finite-dimensional Lie algebras with fixed nilradical (in the capacity of which any nilpotent Lie algebra may serve). We prove an exact estimate for dimensions of Lie algebras from this set. We also show that there may exist several Lie algebras in this set, possessing the maximal dimension. Proofs are based on a concept of algebraic splitting for finite-dimensional Lie algebras.
Keywords: Lie algebra, nilradical, algebraic splitting of the Lie algebra, Chevalley's decomposition.
Received: 26.08.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 2, Pages 29–35
DOI: https://doi.org/10.3103/S1066369X1502005X
Bibliographic databases:
Document Type: Article
UDC: 512.554
Language: Russian
Citation: V. V. Gorbatsevich, “On the maximal finite-dimensional Lie algebras with given nilradical”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 2, 35–44; Russian Math. (Iz. VUZ), 59:2 (2015), 29–35
Citation in format AMSBIB
\Bibitem{Gor15}
\by V.~V.~Gorbatsevich
\paper On the maximal finite-dimensional Lie algebras with given nilradical
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 2
\pages 35--44
\mathnet{http://mi.mathnet.ru/ivm8972}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 2
\pages 29--35
\crossref{https://doi.org/10.3103/S1066369X1502005X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84921884367}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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