On exact Courant algebras

TL;DR

This paper characterizes exact Courant algebras over a Lie algebra using Leibniz 2-cocycles and establishes a correspondence between automorphism groups and Leibniz cohomology.

Contribution

It provides a new characterization of exact Courant algebras via Leibniz cohomology and relates automorphisms to first Leibniz cohomology space.

Findings

Exact Courant algebras are characterized by Leibniz 2-cocycles.

Automorphism groups correspond to first Leibniz cohomology space.

Provides a cohomological perspective on Courant algebras.

Abstract

In this note we will show that exact Courant algebras over a Lie algebra $\mathfrak{g}$ can be characterised via Leibniz $2$- cocycles, and the automorphism group of a given exact Courant algebra is in a one-to-one correspondence with first Leibniz cohomology space of $\mathfrak{g}$.