Non-naturally reductive Einstein metrics on exceptional Lie
groups

J 2017

Non-naturally reductive Einstein metrics on exceptional Lie groups

CHRYSIKOS, Ioannis a Yusuke SAKANE

Základní údaje

Originální název

Non-naturally reductive Einstein metrics on exceptional Lie groups

Autoři

CHRYSIKOS, Ioannis a Yusuke SAKANE

Vydání

Journal of Geometry and Physics, Amsterdam, Elsevier Science BV, 2017, 0393-0440

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10100 1.1 Mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Full Text

Impakt faktor

Impact factor: 0.712

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/17:00112167

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Left-invariant Einstein metrics; Naturally reductive metrics; Exceptional Lie groups; Flag manifolds

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 9. 1. 2020 09:57, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Grobner bases and classify the real solutions of the associated algebraic systems. For the Lie group G(2) we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E-7 and E-8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K)-invariant by different Lie subgroups K.

Citovat

CHRYSIKOS, Ioannis a Yusuke SAKANE. Non-naturally reductive Einstein metrics on exceptional Lie groups. Journal of Geometry and Physics. Amsterdam: Elsevier Science BV, 2017, roč. 116, JUN, s. 152-186. ISSN 0393-0440. Dostupné z: https://doi.org/10.1016/j.geomphys.2017.01.030.

@article{1600969,
   author = {Chrysikos, Ioannis and Sakane, Yusuke},
   article_location = {Amsterdam},
   article_number = {JUN},
   doi = {https://doi.org/10.1016/j.geomphys.2017.01.030},
   keywords = {Left-invariant Einstein metrics; Naturally reductive metrics; Exceptional Lie groups; Flag manifolds},
   language = {eng},
   issn = {0393-0440},
   journal = {Journal of Geometry and Physics},
   title = {Non-naturally reductive Einstein metrics on exceptional Lie groups},
   url = {https://arxiv.org/pdf/1511.03993.pdf},
   volume = {116},
   year = {2017}
}

TY  - JOUR
ID  - 1600969
AU  - Chrysikos, Ioannis - Sakane, Yusuke
PY  - 2017
TI  - Non-naturally reductive Einstein metrics on exceptional Lie groups
JF  - Journal of Geometry and Physics
VL  - 116
IS  - JUN
SP  - 152-186
EP  - 152-186
PB  - Elsevier Science BV
SN  - 03930440
KW  - Left-invariant Einstein metrics
KW  - Naturally reductive metrics
KW  - Exceptional Lie groups
KW  - Flag manifolds
UR  - https://arxiv.org/pdf/1511.03993.pdf
L2  - https://arxiv.org/pdf/1511.03993.pdf
N2  - Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Grobner bases and classify the real solutions of the associated algebraic systems. For the Lie group G(2) we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E-7 and E-8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K)-invariant by different Lie subgroups K.
ER  -

CHRYSIKOS, Ioannis a Yusuke SAKANE. Non-naturally reductive Einstein metrics on exceptional Lie groups. \textit{Journal of Geometry and Physics}. Amsterdam: Elsevier Science BV, 2017, roč.~116, JUN, s.~152-186. ISSN~0393-0440. Dostupné z: https://doi.org/10.1016/j.geomphys.2017.01.030.

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