Speaker
Domenico Fiorenza, Sapienza University of Rome
Abstract
In “$L_\infty$-algebras and higher analogues of Dirac structures and Courant algebroids”, arXiv:1003.1004, Marco Zambon exhibits an explicit $L_\infty$-morphism between the $r=1$ Courant Lie algebra of a smooth manifold $M$, twisted by a closed 2-form $\sigma$, and the $r=2$ untwisted Courant Lie 2-algebra of the same manifold. In the same article it is left as an open question whether there generally exist higher versions of this, i.e. canonical $L_\infty$-morphism between the $r$-Courant Lie algebra of $M$, twisted by a closed $(r+1)$-form $\sigma$, and the untwisted Courant Lie $(r+1)$-algebra of $M$. I will present a general framework indicating why such morphisms should naturally exist. Joint work with Antonio Miti.