Holomorphic string algebroids
Mario Garcia-Fernandez, Roberto Rubio, Carl Tipler
Abstract
We introduce the category of <italic>holomorphic string algebroids</italic> , whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles and whose morphisms correspond to <italic>inner morphisms</italic> of the underlying holomorphic Courant algebroids. This category provides natural candidates for Atiyah Lie algebroids of holomorphic principal bundles for the (complexified) <italic>string group</italic> and their morphisms. Our main results are a classification of string algebroids in terms of Čech cohomology and the construction of a locally complete family of deformations of string algebroids via a differential graded Lie algebra.
Topics & Concepts
MathematicsHolomorphic functionMorphismPure mathematicsCohomologyString (physics)Differential geometryPrincipal (computer security)Lie groupDifferential formAlgebra over a fieldCharacteristic classFiber bundleVector bundleHomology (biology)Differential (mechanical device)String theoryPrincipal bundleLie algebroidHomotopy and Cohomology in Algebraic TopologyAlgebraic structures and combinatorial modelsAdvanced Topics in Algebra