Deformations of pre-symplectic structures and the Koszul L-infty-algebra

Reference : Deformations of pre-symplectic structures and the Koszul L-infty-algebra


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/31775

Title :	Deformations of pre-symplectic structures and the Koszul L-infty-algebra
Language :	English
Author, co-author :	Schätz, Florian [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Zambon, Marco [Katholieke Universiteit Leuven - KUL > Mathematics]
Publication date :	2017
Edition :	2
Number of pages :	44
Peer reviewed :	No
Keywords :	[en] pre-symplectic structures ; Dirac geometry ; deformation theory
Abstract :	[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.
Permalink :	http://hdl.handle.net/10993/31775
source URL :	https://arxiv.org/abs/1703.00290

File(s) associated to this reference

Fulltext file(s):

	File	Commentary	Version	Size	Access
Open access	Kosul_L-infty-algebra_arXiv_VERSION2.pdf		Author preprint	685.29 kB	View/Open

All documents in ORBi^lu are protected by a user license.