Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F18%3A50014873" target="_blank" >RIV/62690094:18470/18:50014873 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs11005-018-1048-1" target="_blank" >https://link.springer.com/article/10.1007%2Fs11005-018-1048-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11005-018-1048-1" target="_blank" >10.1007/s11005-018-1048-1</a>

Result language
angličtina
Original language name
Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids
Original language description
Cartan-Lie algebroids, i.e., Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids with ad-invariant (Riemannian) metrics on their fibers and base k and g, respectively. We determine the necessary and sufficient conditions for a positive quadratic Lie algebroid to integrate to a Riemannian Cartan-Lie groupoid. Here we mean a Cartan-Lie groupoid G equipped with a bi-invariant and inversion-invariant metric eta on TG such that it induces by submersion the metric g on its base and its restriction to the t-fibers coincides with 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
10101 - Pure mathematics

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

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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