Non-naturally reductive Einstein metrics on exceptional Lie groups

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00112167" target="_blank" >RIV/00216224:14310/17:00112167 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/1511.03993.pdf" target="_blank" >https://arxiv.org/pdf/1511.03993.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2017.01.030" target="_blank" >10.1016/j.geomphys.2017.01.030</a>

Result language
angličtina
Original language name
Non-naturally reductive Einstein metrics on exceptional Lie groups
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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