Yunhe Sheng:
Dirac structures of omni-Lie algebroids
In order to characterize Lie algebroid structures on a vector
bundle $E$, Zhuo Chen and Zhangju Liu introduced the notion of omni-Lie
algebroids, which is a generlization of Alan Weinstein's omni-Lie
algebras.
There are three parts in this talk, first I will introduce the notion of
omni-Lie algebroids by using the covariant differential operator bundle
and
the first jet bundle of a vector bundle $E$. Then we study the
properties of
Dirac structures, in particular, Lie algebroid structures on $E$
correspond
to some special Dirac structures of omni-Lie algebroids. At last, I
introduce the notion of $E$-Courant algebroids which is a
generalization of
Courant algebroids introduced by Liu, Weinstein and Xu.