We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including ``three-algebra geometries'', which encode the structure constants for three-algebras and in some cases give novel uplifts for $CSO(p,q,r)$ gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality.

中文翻译：

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探索非凡的 Drinfeld 几何形状

我们探索了产生新代数结构的几何，即异常 Drinfeld 代数，它最近被提出作为研究广义 U 对偶的一种方法，类似于 T 对偶的非阿贝尔和泊松-李概括。这个代数一般不是李代数而是莱布尼茨代数，并且可以通过一组给出广义并行化的框架域在例外广义几何或例外场论中实现。我们提供了包括“三代数几何”在内的例子，它对三代数的结构常数进行编码，并在某些情况下为七维最大超重力的 $CSO(p,q,r)$ 测量提供新的提升。我们还讨论了非阿贝尔和 Poisson-Lie T-对偶的 M 理论嵌入。