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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 6, Pages 86–99 (Mi izv8506)  

Extension of transitive actions of Lie groups

V. V. Gorbatsevich


Abstract: We give an algebraic construction of extensions of arbitrary transitive actions of soluble Lie groups on compact manifolds. The question of the possible dimensions of such extensions is studied in detail. We also consider some generalizations of this construction and the question of constructing extended transitive Lie group actions in some particular cases.

Keywords: soluble Lie group, homogeneous space, solvmanifold, nilmanifold, lattice.

DOI: https://doi.org/10.4213/im8506

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English version:
Izvestiya: Mathematics, 2017, 81:6, 1143–1154

Bibliographic databases:

UDC: 512.816.5
MSC: 22F05, 22E25, 57S20, 14L30, 17B08
Received: 11.01.2016
Revised: 28.06.2016

Citation: V. V. Gorbatsevich, “Extension of transitive actions of Lie groups”, Izv. RAN. Ser. Mat., 81:6 (2017), 86–99; Izv. Math., 81:6 (2017), 1143–1154

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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