Geodesic
Groups associated with minimal flows
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 471-477
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $\widehat{S}$.
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 $\widehat{S}$.
Classification : 54H15, 54H20
Keywords: flow; dynamical system; left congruence; maximal group 
@article{CMJ_2005_55_2_a16,
     author = {Lawson, J. D. and Lisan, Amha T.},
     title = {Groups associated with minimal flows},
     journal = {Czechoslovak Mathematical Journal},
     pages = {471--477},
     year = {2005},
     volume = {55},
     number = {2},
     mrnumber = {2137153},
     zbl = {1081.54032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/}
}
TY  - JOUR
AU  - Lawson, J. D.
AU  - Lisan, Amha T.
TI  - Groups associated with minimal flows
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 471
EP  - 477
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/
LA  - en
ID  - CMJ_2005_55_2_a16
ER  - 
%0 Journal Article
%A Lawson, J. D.
%A Lisan, Amha T.
%T Groups associated with minimal flows
%J Czechoslovak Mathematical Journal
%D 2005
%P 471-477
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/
%G en
%F CMJ_2005_55_2_a16
Lawson, J. D.; Lisan, Amha T. Groups associated with minimal flows. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 471-477. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a16/

[1] J.  Auslander: Minimal Flows and Their Extensions. North-Holland, Amsterdam, 1988. | MR | Zbl

[2] J. E.  Berglund, H. D.  Junghenn and P.  Milnes: Analysis on Semigroups. John Wiley and Sons, New York, 1989. | MR

[3] R. Ellis: Lectures on Topological Dynamics. Benjamin, New York, 1969. | MR | Zbl

[4] J. D. Lawson: Flows and compactifications. J. London Math. Soc. 46 (1992), 349–363. | MR | Zbl

[5] J. D. Lawson and Amha Lisan: Transitive flows: a semigroup approach. Mathematika 38 (1991), 348–361. | DOI | MR

[6] J. D. Lawson and Amha Lisan: Flows, congruences, and factorizations. Topology Appl. 58 (1994), 35–46. | DOI | MR