We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence between such Lie bialgebroid crossed modules and co-quadratic Manin triples (K,P,Q) is established, where K is a co-quadratic Lie algebroid and (P,Q) is a pair of transverse Dirac structures in K.

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关于李双代数交叉模

我们研究李双代数交叉模，它们是对偶的李代数交叉模对，典型地产生李双代数。这样的李双代数交叉模和共二次马宁三元组之间的一一对应关系(ķ,磷,问)成立，其中ķ是一个余二次李代数和(磷,问)是一对横向狄拉克结构ķ.