Lie rackoids integrating Courant algebroids
| Autor: | Camille Laurent-Gengoux, Friedrich Wagemann |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), Université de Nantes (UN) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Standard Courant algebroid 01 natural sciences Courant algebroid Dorfman bracket Leibniz algebroid Poisson manifold 0103 physical sciences FOS: Mathematics Equivalence relation Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Mathematics::Symplectic Geometry Quotient Integration of Courant algebroids Mathematics Lie rackoid Weinstein groupoid 010102 general mathematics Automorphism [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] Lie groupoid Bracket (mathematics) Extended tangent bundle Mathematics - Symplectic Geometry Product (mathematics) [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] Symplectic Lie groupoid Symplectic Geometry (math.SG) 010307 mathematical physics Geometry and Topology Analysis |
| Zdroj: | Annals of Global Analysis and Geometry Annals of Global Analysis and Geometry, Springer Verlag, 2020, 57 (2), pp.225-256. ⟨10.1007/s10455-019-09697-2⟩ |
| ISSN: | 0232-704X 1572-9060 |
| DOI: | 10.1007/s10455-019-09697-2⟩ |
| Popis: | We construct an infinite-dimensional Lie rackoid Y which hosts an integration of the standard Courant algebroid. As a set, $$Y={{\mathcal {C}}}^{\infty }([0,1],T^*M)$$ for a compact manifold M. The rackoid product is by automorphisms of the Dorfman bracket. The first part of the article is a study of the Lie rackoid Y and its tangent Leibniz algebroid, a quotient of which is the standard Courant algebroid. In the second part, we study the equivalence relation related to the quotient on the rackoid level and restrict then to an integrable Dirac structure. We show how our integrating object contains the corresponding integrating Weinstein Lie groupoid in the case where the Dirac structure is given by a Poisson structure. |
| Databáze: | OpenAIRE |
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