"aegis of" is correct and usable in written English.
It's typically used to refer to the protection or support of something else. For example, "The country found shelter under the aegis of a larger ally."
They are under the aegis of the Church.
But under the aegis of dominance, specific expertise is irrelevant.
It is under the aegis of the Ministry of Culture.
All of these places carried the aegis of world heritage.
There is talk of a small executive body under the aegis of the king.
Dillons had already been under the aegis of HMV, and its stores were rebranded as Waterstone's.
The state sector continued to be operated under the aegis of V.S.N.Kh.
The region's five state monuments are under the aegis of the Museum of New Mexico.
The program comes under the aegis of a CBS Corporation unit, CBS EcoMedia.
Under the aegis of capitalism, ownership might be the most powerful intoxicant of all.
But they gathered in France under the aegis of the writers Breton and George Bataille.
