This paper provides an alternative, much simpler, definition for Li-Bland's LA-Courant algebroids, or Poisson Lie 2-algebroids, in terms of split Lie 2-algebroids and self-dual 2-representations. This definition generalises in a precise sense the characterisation of (decomposed) double Lie algebroids via matched pairs of 2-representations. We use the known geometric examples of LA-Courant algebroids in order to provide new examples of Poisson Lie 2-algebroids, and we explain in this general context Roytenberg's equivalence of Courant algebroids with symplectic Lie 2-algebroids. We study further the core of an LA-Courant algebroid and we prove that it carries an induced degenerate Courant algebroid structure. In the nondegenerate case, this gives a new construction of a Courant algebroid from the corresponding symplectic Lie 2-algebroid. Finally we completely characterise VB-Dirac and LA-Dirac structures via simpler objects, that we compare to Li-Bland's pseudo-Dirac structures.

中文翻译：

---

关于 LA-Courant 代数和 Poisson Lie 2-代数

这篇论文为 Li-Bland 的 LA-Courant algebroids 或 Poisson Lie 2-algebroids 提供了一个替代的、更简单的定义，根据分裂 Lie 2-algebroids 和自对偶 2-representations。这个定义在精确的意义上概括了（分解的）双李代数通过匹配的 2 表示对的表征。我们使用 LA-Courant 代数体的已知几何例子来提供 Poisson Lie 2-algebroids 的新例子，并在这个一般上下文中解释 Roytenberg 与辛李 2-algebroids 的 Courant 代数体的等价。我们进一步研究了 LA-Courant 代数体的核心，并证明它具有诱导退化的 Courant 代数体结构。在非退化情况下，这从相应的辛李 2-代数体中给出了一个新的 Courant 代数体构造。