G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality

Abstract

We introduce the notion of G-algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in $E_{n(n)}\times {\mathbb{R}}^{+}$ exceptional generalised geometry for $n\in \{3,\dots ,6\}$. 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.

17 pages, updated references