Geodesic
On a Theorem of D. W. Barnes
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 583-584

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Let L be a solvable Lie algebra and A be an abelian ideal of L. For a ∊ A, let da be the (right) inner derivation of L generated by a and let exp da = 1 + da . Since A is abelian, exp da is an automorphism and exp da exp db = exp da+b for all a, b ∊ A. Let I(L, A) be the subgroup of the automorphism group of L generated by exp da for all a ∊ A. 
Stitzinger, Ernest L. On a Theorem of D. W. Barnes. Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 583-584. doi: 10.4153/CMB-1971-107-0
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[1] 1. Barnes, D. W., On the cohomology of solvable Lie algebras, Math. Z. 101 (1967), 343-349. Google Scholar

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