Domenico Fiorenza: L_infty morphisms between twisted Courant r-Lie algebras and untwisted Courant (r+1)-Lie algeb

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.