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@article{2285839, author = {Alekseevsky, Dmitri and Chrysikos, Ioannis and Galaev, Anton}, article_number = {October}, doi = {http://dx.doi.org/10.1016/j.difgeo.2022.101932}, keywords = {Reductive homogeneous Lorentzian manifolds; Lorentz algebra; Totally reducible subalgebras of the; Lorentz algebra; Admissible subgroups; Contact homogeneous manifolds; Wolf spaces}, language = {eng}, issn = {0926-2245}, journal = {Differential Geometry and its Applications}, note = {Nevykazovat do RIV. Autor nemá afiliaci k MU.}, title = {Reductive homogeneous Lorentzian manifolds}, url = {https://doi.org/10.1016/j.difgeo.2022.101932}, volume = {84}, year = {2022} }
TY - JOUR ID - 2285839 AU - Alekseevsky, Dmitri - Chrysikos, Ioannis - Galaev, Anton PY - 2022 TI - Reductive homogeneous Lorentzian manifolds JF - Differential Geometry and its Applications VL - 84 IS - October SP - 1-21 EP - 1-21 PB - Elsevier Science SN - 09262245 N1 - Nevykazovat do RIV. Autor nemá afiliaci k MU. KW - Reductive homogeneous Lorentzian manifolds KW - Lorentz algebra KW - Totally reducible subalgebras of the KW - Lorentz algebra KW - Admissible subgroups KW - Contact homogeneous manifolds KW - Wolf spaces UR - https://doi.org/10.1016/j.difgeo.2022.101932 N2 - We study homogeneous Lorentzian manifolds M = G/L of a connected reductive Lie group Gmodulo a connected reductive subgroup L, under the assumption that M is (almost) G-effective and the isotropy representation is totally reducible. We show that the description of such manifolds reduces to the case of semisimple Lie groups G. Moreover, we prove that such a homogeneous space is reductive. We describe all totally reducible subgroups of the Lorentz group and divide them into three types. The subgroups of Type Iare compact, while the subgroups of Type II and Type III are non-compact. The explicit description of the corresponding homogeneous Lorentzian spaces of Type II and III(under some mild assumption) is given. We also show that the description of Lorentz homogeneous manifolds M = G/L of Type I reduces to the description of subgroups L such that M = G/Lis an admissible manifold, i.e., an effective homogeneous manifold that admits an invariant Lorentzian metric. Whenever the subgroup Lis a maximal subgroup with these properties, we call such a manifold minimal admissible. We classify all minimal admissible homogeneous manifolds G/L of a compact semisimple Lie group Ga nd describe all invariant Lorentzian metrics on them. ER -
ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS a Anton GALAEV. Reductive homogeneous Lorentzian manifolds. \textit{Differential Geometry and its Applications}. Elsevier Science, 2022, roč.~84, October, s.~1-21. ISSN~0926-2245. Dostupné z: https://dx.doi.org/10.1016/j.difgeo.2022.101932.
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