E-Courant algebroids

TL;DR

This paper introduces $E$-Courant algebroids, a generalized framework encompassing various algebroid structures, and explores their properties, automorphisms, and classifications.

Contribution

It defines $E$-Courant algebroids, studies their automorphisms, classifies exact cases, and introduces related concepts like $E$-Lie bialgebroids and Manin triples.

Findings

Defined $E$-Courant algebroids as a generalization of Courant structures.

Classified isomorphism classes of exact $E$-Courant algebroids.

Analyzed automorphism groups of omni-Lie algebroids.

Abstract

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by $E$-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact $E$-Courant algebroids. In addition, we introduce the concepts of $E$-Lie bialgebroids and Manin triples.