Poisson geometry and Lie $\bm{n}$-algebras

Abstract

There is a close relation between Poisson geometry and higher categorical structures. In this paper, we mainly summarize the relation between Courant algebroids, pre-Courant algebroids and Lie 2-algebras; the relation between $\LWX$ 2-algebroids and Lie 3-algebras; (nonabelian) omni-($n$)-Lie algebras and Lie 2-algebras; multisymplectic geometry and Lie $n$-algebras; isotropic involutive subbundle of higher analogue of Courant algebroids and Lie $n$-algebras.