论文标题
探索杰出的德林菲尔德几何形状
Exploring Exceptional Drinfeld Geometries
论文作者
论文摘要
我们探索引起新的代数结构的几何形状，即特林菲尔德代数的特殊代数，该代数最近被提议作为研究概括U-二元性的一种方法，类似于非阿布莱恩和托儿所的T-二维概括。该代数通常不是Lie代数，而是Leibniz代数，并且可以通过一组框架字段在杰出的广义几何形状或杰出的场理论中实现，从而实现一套具有广义并行化的框架字段。我们提供了包括“三个代数几何形状”在内的示例，该示例编码了三个代数的结构常数，在某些情况下，为$ CSO（P，P，Q，R）$级别的$七维最大超级实力提供了新颖的提升。我们还讨论了非亚洲和泊松lie t二维的理论嵌入。
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.
