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

TL;DR

This paper develops a new algebraic framework for Courant algebroids involving multidifferential operators and Dorfman connections, extending existing structures and enabling geometric identities to be expressed algebraically.

Contribution

It introduces a novel algebra and complex of multidifferential operators for Courant algebroids and explores Dorfman connections, extending the standard algebraic structures.

Findings

Construction of a new algebra and complex of multidifferential operators

Extension of the standard Courant-Dorfman algebra complex

Expression of geometric identities within the new algebraic framework

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.