We introduce the notion of ‐algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in exceptional generalised geometry for . Focusing on the exceptional case, we prove a classification of “exact” algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem. After discussing the general notion of Poisson–Lie duality, we show that the Poisson–Lie U‐duality is compatible with the equations of motion of supergravity.

中文翻译：

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G-Algebroids：异常和广义几何以及泊松-李对偶性的统一框架

我们介绍了-代数的概念，推广了Lie和Courant代数，以及用于的特殊广义几何中的代数。针对特殊情况，我们证明了“精确”代数的分类，并将莱布尼兹可平行空间的相关分类转换为可处理的代数问题。在讨论了泊松-李对偶性的一般概念之后，我们证明了泊松-李对偶性与超重力运动方程是兼容的。