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December 2012 L∞-algebras and higher analogues of Dirac sturctures and Courant albegroids
Marco Zambon
J. Symplectic Geom. 10(4): 563-599 (December 2012).


We define a higher analogue of Dirac structures on a manifold $M$. Under a regularity assumption, higher Dirac structures can be described by a foliation and a (not necessarily closed, non-unique) differential form on $M$, and are equivalent to (and simpler to handle than) the multi-Dirac structures recently introduced in the context of field theory by Vankerschaver et al. We associate an $L_\infty$-algebra of observables to every higher Dirac structure, extending work of Baez et al. on multisymplectic forms. Further, applying a recent result of Getzler, we associate an $L_\infty$-algebra to any manifold endowed with a closed differential form $H$, via a higher analogue of split Courant algebroid twisted by $H$. Finally, we study the relations between the $L_\infty$-algebras appearing above.


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Marco Zambon. "L∞-algebras and higher analogues of Dirac sturctures and Courant albegroids." J. Symplectic Geom. 10 (4) 563 - 599, December 2012.


Published: December 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1260.53134

Rights: Copyright © 2012 International Press of Boston


Vol.10 • No. 4 • December 2012
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