Extending the Campbell-Hausdorff multiplication
type: Item
instance of: scholarly article
title: Extending the Campbell-Hausdorff multiplication
zbMATH Open document ID: 0778.17002
DOI: 10.1007/BF01264092
author: Anselm Eggert
published in: Geometriae Dedicata
publication date: 1994-01-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 205521
zbMATH Keywords: Campbell-Hausdorff series
zbMATH Keywords: solvable Lie algebra
zbMATH Keywords: analytic continuation
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
cites work: Q4095018
cites work: L'application exponentielle dans les groupes de Lie résolubles
cites work: Q4002974
cites work: Q5339349
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description: scientific article; zbMATH DE number 205521