Geodesic
On the maximal finite-dimensional Lie algebras with given nilradical
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 35-44

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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, algebraic splitting of the Lie algebra, Chevalley's decomposition.
Mots-clés : nilradical 
@article{IVM_2015_2_a4,
     author = {V. V. Gorbatsevich},
     title = {On the maximal finite-dimensional {Lie} algebras with given nilradical},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {35--44},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_2_a4/}
}
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V. V. Gorbatsevich. On the maximal finite-dimensional Lie algebras with given nilradical. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 35-44. http://geodesic.mathdoc.fr/item/IVM_2015_2_a4/