Reductive homogeneous Lorentzian manifolds

J 2022

Reductive homogeneous Lorentzian manifolds

ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Anton GALAEV

Basic information

Original name

Reductive homogeneous Lorentzian manifolds

Authors

ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Anton GALAEV

Edition

Differential Geometry and its Applications, Elsevier Science, 2022, 0926-2245

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.500

DOI

http://dx.doi.org/10.1016/j.difgeo.2022.101932

UT WoS

000838919700001

Keywords in English

Reductive homogeneous Lorentzian manifolds; Lorentz algebra; Totally reducible subalgebras of the; Lorentz algebra; Admissible subgroups; Contact homogeneous manifolds; Wolf spaces

Abstract

V originále

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.

Citovat

ALEKSEEVSKY, Dmitri, Ioannis CHRYSIKOS and Anton GALAEV. Reductive homogeneous Lorentzian manifolds. Differential Geometry and its Applications. Elsevier Science, 2022, vol. 84, October, p. 1-21. ISSN 0926-2245. Available from: https://dx.doi.org/10.1016/j.difgeo.2022.101932.

@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 and Anton GALAEV. Reductive homogeneous Lorentzian manifolds. \textit{Differential Geometry and its Applications}. Elsevier Science, 2022, vol.~84, October, p.~1-21. ISSN~0926-2245. Available from: https://dx.doi.org/10.1016/j.difgeo.2022.101932.

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