Abstract
AbstractWe introduce the notion of ‐algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in exceptional generalised geometry for . 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.
Highlights
We introduce the notion of G-algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in En(n) × R+ exceptional generalised geometry for n ∈ {3, ... , 6}
Focusing on the exceptional case, we prove a classification result for exact algebroids and reduce the classification of Leibniz parallelisable spaces to a quite simple algebraic problem
A classification of Leibniz parallelisable Mexact elgebroids translates into a tractable algebraic problem and
Summary
The n-torus compactifications of M-theory exhibit a U-duality symmetry, which features the split real forms of exceptional Lie groups of rank n (as opposed to the split real form of the orthogonal group in the T-duality case). A Poisson–Lie-type generalisation of U-duality was first proposed and investigated in the case without spectators in [19, 22]. One of the goals of this paper is to describe this phenomenon in the language of algebroids, allowing the employment of techniques and strategies known from Courant algebroids. This will involve defining a suitable non-exact generalisation of the algebroids that appear in exceptional generalised geometry
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