The equivalent metric form of this is to write a group element g ∈ ∈ G as the geodesic g = exp ⁡ ⁡ ( θ θ i T i ) of an element θ θ i T i ∈ ∈ g of the Lie algebra g . The [ T i , T j ] = f i j k T k are the basis elements for the Lie algebra; the f i j k are the structure constants of g .