G-Algebroids : A Unified Framework for Exceptional and Generalised Geometry, and Poisson-Lie Duality
Bugden, Mark, Hulík, Ondřej, Valach, Fridrich, Waldram, Daniel
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.
Topics & Concepts
Duality (order theory)MathematicsPoisson distributionLie algebroidSupergravityPure mathematicsT-dualityAlgebra over a fieldLie algebraMathematical physicsSupersymmetryStatisticsString theoryHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in AlgebraNonlinear Waves and Solitons