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

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