Cartan Geometries and their Symmetries: A Lie Algebroid Approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F16%3AA1701J0H" target="_blank" >RIV/61988987:17310/16:A1701J0H - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Cartan Geometries and their Symmetries: A Lie Algebroid Approach

Popis výsledku v původním jazyce

'A Cartan geometry is a Klein geometry with curvature': that is, given a Klein geometry as a homogeneous space G/H where G is a Lie group and H a closed Lie subgroup, a Cartan geometry is a smooth manifold M which locally is 'like G/H'. A modern approach to Cartan geometry is given in a book by Sharpe, where the structure is given by a principal H-bundle over M and a 'Cartan connection', a 1-form on M taking values in the Lie algebra of G (rather than H). This book describes an alternative approach to Cartan geometry starting with, rather than a principal bundle, a fibre bundle with standard fibre G/H. The morphisms of this structure form a Lie groupoid with a distinguished Lie subgroupoid, and the geometry is given by a path connection. The corresponding infinitesimal structures are Lie algebroids and an infi nitesimal connection. An advantage of this approach is that the Lie algebroids obtained in this way can be identi ed with certain Lie algebroids of projectable vector fi elds on the fibre bundle. This gives a means of relating the present approach to those classical studies of projective and conformal geometry which used methods of tensor calculus. An extension of this method can also be used to study the more general projective geometry of sprays.

Název v anglickém jazyce

Cartan Geometries and their Symmetries: A Lie Algebroid Approach

Popis výsledku anglicky

'A Cartan geometry is a Klein geometry with curvature': that is, given a Klein geometry as a homogeneous space G/H where G is a Lie group and H a closed Lie subgroup, a Cartan geometry is a smooth manifold M which locally is 'like G/H'. A modern approach to Cartan geometry is given in a book by Sharpe, where the structure is given by a principal H-bundle over M and a 'Cartan connection', a 1-form on M taking values in the Lie algebra of G (rather than H). This book describes an alternative approach to Cartan geometry starting with, rather than a principal bundle, a fibre bundle with standard fibre G/H. The morphisms of this structure form a Lie groupoid with a distinguished Lie subgroupoid, and the geometry is given by a path connection. The corresponding infinitesimal structures are Lie algebroids and an infi nitesimal connection. An advantage of this approach is that the Lie algebroids obtained in this way can be identi ed with certain Lie algebroids of projectable vector fi elds on the fibre bundle. This gives a means of relating the present approach to those classical studies of projective and conformal geometry which used methods of tensor calculus. An extension of this method can also be used to study the more general projective geometry of sprays.

Druh

B - Odborná kniha

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-02476S" target="_blank" >GA14-02476S: Variace, geometrie a fyzika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-94-6239-191-8

Počet stran knihy

290

Název nakladatele

Atlantis Press

Místo vydání

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Kód UT WoS knihy

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