H-twisted Lie algebroids

Abstract

We define a new kind of algebroid which fulfills a Leibniz rule, a Jacobi identity twisted by a 3-form $H$ with values in the kernel of the anchor map, and the twist is closed under a naturally occurring exterior covariant derivative. We give examples and define three kinds of cohomology two via realization as Q-structure on graded manifolds. This classifies PQ3-manifolds.

18 pages, improvements due to the referee, to appear in Journal of Geometry and Physics

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• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• The geometry of graded cotangent bundles
• Quantization of Magnetic Poisson Structures
• Metric-Connection Geometries on Pre-Leibniz Algebroids: A Search for Geometrical Structure in String Models
• Donaldson Invariants and Their Generalizations from AKSZ Topological Field Theories
• H-twisted Courant algebroids
• Cohomology for almost Lie algebroids
• Brane current algebras and generalised geometry from QP manifolds
• 'Anti-Commutable' Pre-Leibniz Algebroids and Admissible Connections
• Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
• Categorification of VB-Lie algebroids and VB-Courant algebroids