Extending the Campbell-Hausdorff multiplication
The author gives a sufficient condition for extending the Campbell- Hausdorff multiplication in a Lie algebra to a much larger open set. Let \(I\) be an ideal of a finite-dimensional Lie algebra such that \(2\pi i\) is not an eigenvalue of \(\text{ad} X\) for all \(X\) in \(I\). Then there exists an open ball \(V\) around 0 such that the Campbell-Hausdorff multiplication admits an analytic extension to \((I+V)\times (I+V)\). This generalizes an old result of Dixmier and provides a new and easier proof.
scientific article; zbMATH DE number 205521