Geodesic
Compact Elements in Connected Lie Groups
Mikhail Kabenyuk1
1Institute of Fundamental Sciences, Kemerovo State University, 650043 Kemerovo, Russia
Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 569-578

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that the set of compact elements in the group extension of the 3-dimensional Heisenberg group by SO(2) (the so-called oscillator group) is not dense. We also give a new proof of the following criterion: The set of compact elements of a connected Lie group G is dense in G if and only if every Cartan subgroup of G is compact.
Classification : 22C05, 22E15, 22E25
Mots-clés : Lie group, compact element, Heisenberg group, oscillator group, Cartan subgroup

Mikhail Kabenyuk  1

1 Institute of Fundamental Sciences, Kemerovo State University, 650043 Kemerovo, Russia 
Mikhail Kabenyuk. Compact Elements in Connected Lie Groups. Journal of Lie Theory, Tome 27 (2017) no. 2, pp. 569-578. http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a13/
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     author = {Mikhail Kabenyuk},
     title = {Compact {Elements} in {Connected} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {569--578},
     year = {2017},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_2_a13/}
}
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