Contact Courant algebroids and $L_{\infty }$-algebras

Abstract

Let $L$ be a line bundle over $M$. In this paper we associate an $L_{\infty }$-algebra to any $L$-Courant algebroid (contact Courant algebroid in the sense of Grabowski). This construction is similar to the work of Roytenberg and Weinstein for Courant algebroids. Next we associate a $p$-term $L_{\infty }$-algebra to any isotropic involutive subbundle of $(\mathbb{D}L{)}^p:=DL\oplus ({\wedge }^p(DL{)}^{\ast }\otimes L)$, where $DL$ is the gauge algebroid of $L$. In a particular case, we relate these $L_{\infty }$-algebras by a suitable morphism.

19 pages, comments are welcome