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arXiv · 2006.12452

Exploring Exceptional Drinfeld Geometries

Chris D. A. Blair·Daniel C. Thompson·Sofia Zhidkova
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Abstract

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.

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Chris D. A. Blair, Daniel C. Thompson, Sofia Zhidkova. 2020-06-22. Exploring Exceptional Drinfeld Geometries. https://doi.org/10.1007/jhep09(2020)151

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