G‐Algebroids: A Unified Framework for Exceptional and Generalised Geometry, and Poisson–Lie Duality
Mark Bugden, Ondřej Hulík, Fridrich Valach, Daniel Waldram
Abstract
Abstract We 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.
Topics & Concepts
MathematicsDuality (order theory)Algebra over a fieldAlgebraic numberPure mathematicsMotion (physics)Algebraic structureClass (philosophy)Algebraic propertiesCalculus (dental)Homotopy and Cohomology in Algebraic TopologyNonlinear Waves and SolitonsAlgebraic and Geometric Analysis