On Exact Courant Algebras

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.

Key Words:

• Courant algebra
• Cohomology of Leibniz algebras
• Leibniz algebra
• Lie algebra

2010 Mathematics Subject Classification:

• 17B55
• 17D

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 [11] and a discussion of some unified product for Leibniz algebras is in [1]. One can view Proposition 3.4 and Theorem 4.2 in the present article as special cases in those general consideration.