Geodesic
Moment Map and Gelfand Transform for the Enveloping Algebra
Journal of Lie theory, Tome 29 (2019) no. 1, pp. 227-237
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Describing the Gelfand construction for the analytic states on an universal enveloping algebra, we characterize pure states and re-find the main result of a preceding work with L. Abdelmoula and J. Ludwig on the separation of unitary irreducible representations of a connected Lie group by their generalized moment sets.
Classification : 22D10, 22D20, 52A05
Mots-clés : Universal enveloping algebra, analytic states, moment set of a representation 
@article{JLT_2019_29_1_JLT_2019_29_1_a9,
     author = {D. Arnal and M. Selmi},
     title = {Moment {Map} and {Gelfand} {Transform} for the {Enveloping} {Algebra}},
     journal = {Journal of Lie theory},
     pages = {227--237},
     year = {2019},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_1_JLT_2019_29_1_a9/}
}
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D. Arnal; M. Selmi. Moment Map and Gelfand Transform for the Enveloping Algebra. Journal of Lie theory, Tome 29 (2019) no. 1, pp. 227-237. http://geodesic.mathdoc.fr/item/JLT_2019_29_1_JLT_2019_29_1_a9/