Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes

Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such sp...
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Autor*in:	Figueroa-O’Farrill, José [verfasserIn] Grassie, Ross Prohazka, Stefan

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Space-Time Symmetries Differential and Algebraic Geometry

Anmerkung:	© The Author(s) 2019

Übergeordnetes Werk:	Enthalten in: Journal of high energy physics - Berlin : Springer, 1997, 2019(2019), 8 vom: 22. Aug.
Übergeordnetes Werk:	volume:2019 ; year:2019 ; number:8 ; day:22 ; month:08

Links:	Volltext

DOI / URN:	10.1007/JHEP08(2019)119

Katalog-ID:	SPR030590744

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allfields	10.1007/JHEP08(2019)119 doi (DE-627)SPR030590744 (SPR)JHEP08(2019)119-e DE-627 ger DE-627 rakwb eng Figueroa-O’Farrill, José verfasserin (orcid)0000-0002-9308-9360 aut Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213 Grassie, Ross aut Prohazka, Stefan (orcid)0000-0002-3925-3983 aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2019(2019), 8 vom: 22. Aug. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2019 year:2019 number:8 day:22 month:08 https://dx.doi.org/10.1007/JHEP08(2019)119 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 2019 8 22 08
spelling	10.1007/JHEP08(2019)119 doi (DE-627)SPR030590744 (SPR)JHEP08(2019)119-e DE-627 ger DE-627 rakwb eng Figueroa-O’Farrill, José verfasserin (orcid)0000-0002-9308-9360 aut Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213 Grassie, Ross aut Prohazka, Stefan (orcid)0000-0002-3925-3983 aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2019(2019), 8 vom: 22. Aug. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2019 year:2019 number:8 day:22 month:08 https://dx.doi.org/10.1007/JHEP08(2019)119 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 2019 8 22 08
allfields_unstemmed	10.1007/JHEP08(2019)119 doi (DE-627)SPR030590744 (SPR)JHEP08(2019)119-e DE-627 ger DE-627 rakwb eng Figueroa-O’Farrill, José verfasserin (orcid)0000-0002-9308-9360 aut Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213 Grassie, Ross aut Prohazka, Stefan (orcid)0000-0002-3925-3983 aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2019(2019), 8 vom: 22. Aug. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2019 year:2019 number:8 day:22 month:08 https://dx.doi.org/10.1007/JHEP08(2019)119 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 2019 8 22 08
allfieldsGer	10.1007/JHEP08(2019)119 doi (DE-627)SPR030590744 (SPR)JHEP08(2019)119-e DE-627 ger DE-627 rakwb eng Figueroa-O’Farrill, José verfasserin (orcid)0000-0002-9308-9360 aut Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213 Grassie, Ross aut Prohazka, Stefan (orcid)0000-0002-3925-3983 aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2019(2019), 8 vom: 22. Aug. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2019 year:2019 number:8 day:22 month:08 https://dx.doi.org/10.1007/JHEP08(2019)119 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 2019 8 22 08
allfieldsSound	10.1007/JHEP08(2019)119 doi (DE-627)SPR030590744 (SPR)JHEP08(2019)119-e DE-627 ger DE-627 rakwb eng Figueroa-O’Farrill, José verfasserin (orcid)0000-0002-9308-9360 aut Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2019 Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213 Grassie, Ross aut Prohazka, Stefan (orcid)0000-0002-3925-3983 aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2019(2019), 8 vom: 22. Aug. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2019 year:2019 number:8 day:22 month:08 https://dx.doi.org/10.1007/JHEP08(2019)119 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 2019 8 22 08
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author	Figueroa-O’Farrill, José
spellingShingle	Figueroa-O’Farrill, José misc Space-Time Symmetries misc Differential and Algebraic Geometry Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
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topic_title	Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes Space-Time Symmetries (dpeaa)DE-He213 Differential and Algebraic Geometry (dpeaa)DE-He213
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title	Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
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title_full	Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
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title_sort	geometry and bms lie algebras of spatially isotropic homogeneous spacetimes
title_auth	Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
abstract	Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. © The Author(s) 2019
abstractGer	Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. © The Author(s) 2019
abstract_unstemmed	Abstract Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these “maximally symmetric” spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated vielbein and any invariant aristotelian, galilean or carrollian structures. The (conformal) symmetries of the galilean and carrollian structures we determine are typically infinite-dimensional and reminiscent of BMS Lie algebras. We also determine the space of invariant affine connections on each homogeneous spacetime and work out their torsion and curvature. © The Author(s) 2019
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title_short	Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
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