Geodesic
On locally boundedly exactly doubly transitive lie groups of transformations of the space with a subgroup of parallel translations
Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 126-148.

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The paper solves the problem of extending the group of parallel translations of a three-dimensional space to a locally boundedly exactly doubly transitive group of transformations for the case of a decomposable Lie algebra. The Lie algebra of the required Lie group of transformations is represented as a semidirect sum of a commutative three-dimensional ideal and a three-dimensional Lie subalgebra. Basis operators are found for all Lie algebras of doubly transitive Lie groups of transformations with a subgroup of parallel translations. The Lie groups of transformations are restored from the basis operators. 
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V. A. Kyrov. On locally boundedly exactly doubly transitive lie groups of transformations of the space with a subgroup of parallel translations. Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 126-148. http://geodesic.mathdoc.fr/item/MT_2022_25_2_a4/

[1] Gorbatsevich V.V., “Extension of transitive actions of Lie groups”, Izv. Math., 81:6 (2017), 1143–1154 | DOI | MR | Zbl

[2] Mikhailichenko G.G., Gruppovaya simmetriya fizicheskikh ctruktur, Barn. gos. ped. un-t, Barnaul, 2003

[3] Kyrov V.A., Mikhailichenko G. G., “Vlozhenie additivnoi dvumetricheskoi fenomenologicheski simmetrichnoi geometrii dvukh mnozhestv ranga (2,2) v dvumetricheskie fenomenologicheski simmetrichnye geometrii dvukh mnozhestv ranga (3,2)”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:3 (2018), 305–327 | DOI | MR | Zbl

[4] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980

[5] Kyrov V.A., “K voprosu o lokalnom rasshirenii gruppy parallelnykh perenosov trekhmernogo prostranstva”, Vladikavk. matem. zhurn., 23:1 (2021), 32–42 | DOI | MR | Zbl

[6] Ovsyannikov L.V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[7] Kostrikin A.I., Vvedenie v algebru, Nauka, M., 1977 | MR

[8] Turkowski P., “Lowdimensional real Lie algebras”, J. Math. Phys., 29:10 (1988), 2139–2144 | DOI | MR | Zbl

[9] Morozov V.V., “Klassifikatsiya nilpotentnykh algebr Li shetogo poryadka”, Izv. vuzov. Matem., 1958, no. 4, 161–171 | Zbl

[10] Mubarakzyanov G.M., “O razreshimykh algebrakh Li”, Izv. vuzov. Matem., 1963, no. 1, 114–123 | Zbl

[11] Mubarakzyanov G.M., “Klassifikatsiya razreshimykh algebr Li shestogo poryadka s odnim nenilpotentnym bazisnym elementom”, Izv. vuzov. Matem., 1963, no. 4, 104–116 | MR | Zbl

[12] Turkowski P., “Solvable Lie algebras of dimension six”, J. Math. Phys., 31:6 (1990), 1344–1350 | DOI | MR | Zbl

[13] Kyrov V.A., Bogdanova R.A., “Gruppy dvizhenii nekotorykh trekhmernykh geometrii maksimalnoi podvizhnosti”, Sib. matem. zhurn., 59:2 (2018), 412–421 | DOI | MR | Zbl