Abstract
In this note, we will show that exact Courant algebras over a Lie algebra 𝔤 can be characterized 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 𝔤.
ACKNOWLEDGMENTS
After having posted the paper on the Archive, Prof. G. Militaru kindly mentioned that a more general study of Leibniz algebra extension have been considered in [Citation11] and a discussion of some unified product for Leibniz algebras is in [Citation1]. One can view Proposition 3.4 and Theorem 4.2 in the present article as special cases in those general consideration.