H-standard cohomology for Courant-Dorfman algebras and Leibniz algebras

TL;DR

This paper introduces H-standard cohomology for Courant-Dorfman and Leibniz algebras, generalizes existing theorems, and explores their relations, advancing the theoretical understanding of these algebraic structures.

Contribution

It generalizes Roytenberg's construction of H-standard cohomology and extends a theorem on transitive Courant algebroids, connecting Leibniz algebra complexes with crossed products.

Findings

Established H-standard cohomology for Courant-Dorfman and Leibniz algebras.

Generalized a theorem on transitive Courant algebroids.

Explored the relation between Leibniz algebra complexes and crossed products.

Abstract

We introduce the notion of H-standard cohomology for Courant-Dorfman algebras and Leibniz algebras, by generalizing Roytenberg's construction. Then we generalize a theorem of Ginot-Grutzmann on transitive Courant algebroids, which was conjectured by Stienon-Xu. The relation between H-standard complexes of a Leibniz algebra and the associated crossed product is also discussed.