Symplectic structures on the integration of exact Courant algebroids

Rajan Amit Mehta; Xiang Tang

doi:10.1016/j.geomphys.2018.02.001

Symplectic structures on the integration of exact Courant algebroids

Rajan Amit Mehta
, Xiang Tang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn–Crainic–Weinstein–Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.

Original language	English
Pages (from-to)	68-83
Number of pages	16
Journal	Journal of Geometry and Physics
Volume	127
DOIs	https://doi.org/10.1016/j.geomphys.2018.02.001
State	Published - Apr 2018

Keywords

2-groupoids
Courant algebroids
Dirac
Symplectic

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10.1016/j.geomphys.2018.02.001

Cite this

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title = "Symplectic structures on the integration of exact Courant algebroids",

abstract = "We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn–Crainic–Weinstein–Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.",

keywords = "2-groupoids, Courant algebroids, Dirac, Symplectic",

author = "Mehta, \{Rajan Amit\} and Xiang Tang",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

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T1 - Symplectic structures on the integration of exact Courant algebroids

AU - Mehta, Rajan Amit

AU - Tang, Xiang

PY - 2018/4

Y1 - 2018/4

N2 - We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn–Crainic–Weinstein–Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.

AB - We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn–Crainic–Weinstein–Zhu that every integrable Dirac structure integrates to a presymplectic groupoid.

KW - 2-groupoids

KW - Courant algebroids

KW - Dirac

KW - Symplectic

UR - https://www.scopus.com/pages/publications/85044633684

U2 - 10.1016/j.geomphys.2018.02.001

DO - 10.1016/j.geomphys.2018.02.001

M3 - Article

AN - SCOPUS:85044633684

SN - 0393-0440

VL - 127

SP - 68

EP - 83

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Symplectic structures on the integration of exact Courant algebroids

Abstract

Keywords

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