The Topological Generating Rank of Solvable Lie Groups

Abels H, Noskov GA (2019)
JOURNAL OF LIE THEORY 29(2): 457-471.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
;
Abstract / Bemerkung
We define the topological generating rank d (G) of a connected Lie group G as the minimal number of elements of G needed to generate a dense subgroup of G. We answer the following question posed by K. H. Hofmann and S.A. Morris [see: Finitely generated connected locally compact groups, J. Lie Theory (formerly Sem. Sophus Lie) 2(2) (1992) 123-134]: What is the topological generating rank of a connected solvable Lie group? If G is solvable we can reduce the question to the case that G is metabelian. We can furthermore reduce to the case that the natural representation of Q:= G(ab):= G/(G') over bar on A := (G') over bar is semisimple. Then d (G) is the maximum of the following two numbers: d (Q) and one plus the maximum of the multiplicities of the non-trivial isotypic components of the RQ-module A.
Stichworte
Lie group; solvable; nilpotent; metabelian; topological generators; generating rank
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF LIE THEORY
Band
29
Ausgabe
2
Seite(n)
457-471
ISSN
0949-5932
Page URI
https://pub.uni-bielefeld.de/record/2935885

Zitieren

Abels H, Noskov GA. The Topological Generating Rank of Solvable Lie Groups. JOURNAL OF LIE THEORY. 2019;29(2):457-471.
Abels, H., & Noskov, G. A. (2019). The Topological Generating Rank of Solvable Lie Groups. JOURNAL OF LIE THEORY, 29(2), 457-471.
Abels, H., and Noskov, G. A. (2019). The Topological Generating Rank of Solvable Lie Groups. JOURNAL OF LIE THEORY 29, 457-471.
Abels, H., & Noskov, G.A., 2019. The Topological Generating Rank of Solvable Lie Groups. JOURNAL OF LIE THEORY, 29(2), p 457-471.
H. Abels and G.A. Noskov, “The Topological Generating Rank of Solvable Lie Groups”, JOURNAL OF LIE THEORY, vol. 29, 2019, pp. 457-471.
Abels, H., Noskov, G.A.: The Topological Generating Rank of Solvable Lie Groups. JOURNAL OF LIE THEORY. 29, 457-471 (2019).
Abels, Herbert, and Noskov, Gennady A. “The Topological Generating Rank of Solvable Lie Groups”. JOURNAL OF LIE THEORY 29.2 (2019): 457-471.