Product decompositions of solvable Lie groups
type: Item
instance of: scholarly article
title: Product decompositions of solvable Lie groups
zbMATH Open document ID: 0870.22006
DOI: 10.1007/BF02567948
author: Michael Wüstner
published in: Manuscripta Mathematica
publication date: 1997-09-15T00:00:00Z
full work available at URL: https://eudml.org/doc/156223
review text: The author studies the structure of real connected solvable Lie groups by decomposing them into a direct or semidirect product of factors introduced by the central or compact embedding property combined with the commutator subgroup. It is well known [cf. \textit{C. Chevalley}, Annals of Math., II. Ser. 42, 668-675 (1941; Zbl 0025.24301)] that any such Lie group is homeomorphic to the product of a torus and a cartesian space. In this paper various product decompositions are studied not only by their topological structure but also by their algebraic structure. Leading notions are Cartan algebras (groups), compact elements in Lie algebras (groups) [cf. \textit{K. H. Hofmann}, Semin. Sophus Lie 2, 41-55 (1992; Zbl 0857.17007)] and compactly embedded subalgebras (subgroups). The author uses these notions combined with those of the center and of the commutator subgroup to introduce product factors and proves several factorization results. The results of \textit{M. Goto} [Annals of Math., II. Ser. 61, 154-169 (1955; Zbl 0064.25802)] are essentially used in some points of the proofs.
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 980688
zbMATH Keywords: compactly embedded subalgebras
zbMATH Keywords: compactly embedded subgroups
zbMATH Keywords: solvable Lie groups
zbMATH Keywords: product decompositions
zbMATH Keywords: Cartan algebras
zbMATH Keywords: Lie algebras
Wikidata QID: Q115392019
reviewed by: Hidenori Fujiwara
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 980688