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

TL;DR

This paper introduces G-algebroids, a unified mathematical framework that generalizes existing structures in exceptional and generalised geometry, and explores their relation to Poisson-Lie duality and supergravity equations.

Contribution

It defines G-algebroids as a unifying concept, classifies exact algebroids in the exceptional case, and demonstrates the compatibility of Poisson-Lie U-duality with supergravity equations.

Findings

Classification of exact G-algebroids for n=3,...,6

Translation of Leibniz parallelisable space classification into algebraic problems

Poisson-Lie U-duality is compatible with supergravity equations

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.