Reference : Deformations of pre-symplectic structures and the Koszul L-infty-algebra |
E-prints/Working papers : Already available on another site | |||
Physical, chemical, mathematical & earth Sciences : Mathematics | |||
http://hdl.handle.net/10993/31775 | |||
Deformations of pre-symplectic structures and the Koszul L-infty-algebra | |
English | |
Schätz, Florian ![]() | |
Zambon, Marco [Katholieke Universiteit Leuven - KUL > Mathematics] | |
2017 | |
2 | |
44 | |
No | |
[en] pre-symplectic structures ; Dirac geometry ; deformation theory | |
[en] We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_\infty$-algebra, which we call the Koszul $L_\infty$-algebra. This
$L_\infty$-algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold, and its proper geometric understanding relies on Dirac geometry. In addition, we show that a quotient of the Koszul $L_{\infty}$-algebra is isomorphic to the $L_\infty$-algebra which controls the deformations of the underlying characteristic foliation. Finally, we show that the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed. | |
http://hdl.handle.net/10993/31775 | |
https://arxiv.org/abs/1703.00290 |
File(s) associated to this reference | ||||||||||||||
Fulltext file(s):
| ||||||||||||||
All documents in ORBilu are protected by a user license.