| Title:
|
Groups associated with minimal flows (English) |
| Author:
|
Lawson, J. D. |
| Author:
|
Lisan, Amha T. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
471-477 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $S$ be topological semigroup, we consider an appropriate semigroup compactification $\widehat{S}$ of $S$. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of $\widehat{S}$, which arise as equivalence classes of some closed left congruence, and the minimal flow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on $\widehat{S}$. (English) |
| Keyword:
|
flow |
| Keyword:
|
dynamical system |
| Keyword:
|
left congruence |
| Keyword:
|
maximal group |
| MSC:
|
54H15 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 1081.54032 |
| idMR:
|
MR2137153 |
| . |
| Date available:
|
2009-09-24T11:24:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127993 |
| . |
| Reference:
|
[1] J. Auslander: Minimal Flows and Their Extensions.North-Holland, Amsterdam, 1988. Zbl 0654.54027, MR 0956049 |
| Reference:
|
[2] J. E. Berglund, H. D. Junghenn and P. Milnes: Analysis on Semigroups.John Wiley and Sons, New York, 1989. MR 0999922 |
| Reference:
|
[3] R. Ellis: Lectures on Topological Dynamics.Benjamin, New York, 1969. Zbl 0193.51502, MR 0267561 |
| Reference:
|
[4] J. D. Lawson: Flows and compactifications.J. London Math. Soc. 46 (1992), 349–363. Zbl 0769.54045, MR 1182489 |
| Reference:
|
[5] J. D. Lawson and Amha Lisan: Transitive flows: a semigroup approach.Mathematika 38 (1991), 348–361. MR 1147834, 10.1112/S0025579300006690 |
| Reference:
|
[6] J. D. Lawson and Amha Lisan: Flows, congruences, and factorizations.Topology Appl. 58 (1994), 35–46. MR 1280709, 10.1016/0166-8641(94)90072-8 |
| . |
