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On decompositions and transitive actions of nilpotent Lie groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2024), pp. 3-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article considers decompositions of nilpotent Lie algebras and nilpotent Lie groups, and connections between them. Also, descriptions of irreducible transitive actions of nilpotent Lie groups on the plane and on three-dimensional space are given.
Keywords: nilpotency, Lie algebra
Mots-clés : Lie group, decomposition, exact decomposition. 
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V. V. Gorbatsevich. On decompositions and transitive actions of nilpotent Lie groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2024), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2024_4_a0/

[1] Gorbatsevich V.V., “O trekhmernykh odnorodnykh prostranstvakh”, Sib. matem. zhurn., 18:2 (1977), 280–293 | MR

[2] Vinberg E.B., Gorbatsevich V.V., Onischik A.L., “Stroenie grupp i algebr Li”, Gruppy Li i algebry Li – $3$, Itogi nauki i tekhn. Ser. Sovrem. probl. matem. Fundam. napravleniya, 41, VINITI, M., 1990, 5–253 | MR

[3] Onischik A.L., “Otnosheniya vklyucheniya mezhdu tranzitivnymi kompaktnymi gruppami preobrazovanii”, Tr. Mosk. matem. o-va, 11, 1962, 199–242

[4] Maltsev A.I., “Ob odnom klasse odnorodnykh prostranstv”, Izv. AN SSSR. Ser. matem., 13:1 (1949), 9–32

[5] Agore A.L., Militaru G., “Classifiyng complements for Hopf algebras and Lie algebras”, J. Algebra, 2013, no. 391, 193–208 | DOI | MR

[6] Onischik A.L., “Razlozheniya reduktivnykh grupp Li”, Matem. sb., 80:4 (1969), 553–599

[7] Malyshev F.M., “O razlozheniyakh nilpotentnykh algebr Li”, Matem. zametki, 23:1 (1978), 27–30 | MR

[8] Doubrov B., Three-dimensional homogeneous spaces with non-solvable transformation groups, arXiv: 1704.04393v1

[9] Mostow G., “The Extensibility of Local Lie Groups of Transformations and Groups on Surfaces”, Ann. Math., 52 (1950), 606–636 | DOI | MR

[10] Gelfand I.M., Ponomarev V.A., “Zamechaniya o klassifikatsii pary kommutiruyuschikh lineinykh preobrazovanii v konechnomernom prostranstve”, Funkts. analiz i ego pril., 3:4 (1969), 81–82 | MR

[11] Belitskii G.R., Sergeichuk V.V., “Complexity of matrix problems”, Linear Algebra Appl., 361 (2003), 203–222 | DOI | MR