Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids

Abstract

We construct an algebra and a complex of multidifferential operators on tensor products of a Courant algebroid E with values in the endomorphism bundle of a smooth vector bundle B, predual of E, extending the standard complex of the Courant-Dorfman algebra of E. Also, we study Dorfman connections of E on B, and show that the Cartan calculus, curvatures of induced connections and basic differential geometric identities of them make sense in this algebra.

arXiv commentThe latter version was split, this is the final form of the first part with some additions

References in corpus (12)

• Courant algebroids, derived brackets and even symplectic supermanifolds
• On the first order operators in bimodules
• On Regular Courant Algebroids
• Poisson-Lie T-duality and Courant algebroids
• Ricci flow, Courant algebroids, and renormalization of Poisson--Lie T-duality
• Courant-Dorfman algebras and their cohomology
• Courant Algebroids. A Short History
• Matched pairs of Courant algebroids
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
• Almost regular Poisson manifolds and their holonomy groupoids
• On higher-dimensional Courant algebroids