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Full-Text Articles in Physical Sciences and Mathematics
Constant Symplectic 2-Groupoids, Rajan Amit Mehta, Xiang Tang
Constant Symplectic 2-Groupoids, Rajan Amit Mehta, Xiang Tang
Mathematics Sciences: Faculty Publications
We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the constant symplectic 2-groupoids are, up to equivalence, in one-to-one correspondence with a simple class of Courant algebroids that we call constant Courant algebroids. Furthermore, we find a correspondence between certain Dirac structures and Lagrangian sub-2-groupoids.
Symplectic Structures On The Integration Of Exact Courant Algebroids, Rajan Amit Mehta, Xiang Tang
Symplectic Structures On The Integration Of Exact Courant Algebroids, Rajan Amit Mehta, Xiang Tang
Mathematics Sciences: Faculty Publications
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.