Geodesic
Compact Elements in Connected Lie Groups
Journal of Lie theory, Tome 27 (2017) no. 2, pp. 569-578
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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 
@article{JLT_2017_27_2_JLT_2017_27_2_a13,
     author = {M. 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/JLT_2017_27_2_JLT_2017_27_2_a13/}
}
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M. Kabenyuk. Compact Elements in Connected Lie Groups. Journal of Lie theory, Tome 27 (2017) no. 2, pp. 569-578. http://geodesic.mathdoc.fr/item/JLT_2017_27_2_JLT_2017_27_2_a13/