Geodesic
On~the envelopes of Abelian subgroups in connected Lie groups
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 200-210.

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An Abelian subgroup $A$ in a Lie group $G$ is said to be regular if it belongs to a connected Abelian subgroup $C$ of the group $G$ (then $C$ is called an envelope of $A$). A strict envelope is a minimal element in the set of all envelopes of the subgroup $A$. We prove a series of assertions on the envelopes of Abelian subgroups. It is shown that the centralizer of a subgroup $A$ in $G$ is transitive on connected components of the space of all strict envelopes of $A$. We give an application of this result to the description of reductions of completely integrable equations on a torus to equations with constant coefficients. 
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     title = {On~the envelopes of {Abelian} subgroups in connected {Lie} groups},
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V. V. Gorbatsevich. On~the envelopes of Abelian subgroups in connected Lie groups. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 200-210. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a5/

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