TITLE: Curvature of a Lie group
QUESTION [20 upvotes]: Since a lie group is a manifold with the structure of a continuous group, then each point of the manifold [Edit: provided we fix a metric, for example an invariant or bi-invariant one] has some scalar curvature R.  

Question [Edited] Is there a nice formula which expresses the scalar curvature at a point of the manifold in terms of the lie algebra of the group?

REPLY [11 votes]: For left-invariant (or right-invariant) metrics, this paper of Arnold gives a formula for  the sectional and Riemannian curvatures, in terms of the adjoint of the Lie bracket operation in the metric.