I Have Promoted A Few People In My Team Who Are Now Managing The Same People They Earlier Used To Work With. This Is Causing A Lot Of Friction. How Can I Address This?

"In this situation, it is critical that you manage both sides well. Those who have not been promoted, need to know why others have been promoted. You need to have honest but positive conversations with them on what makes one high-potential and how they can also get there. Make sure you keep their morale high and motivate them.
On the other hand, you must train the new managers well, especially on people management front. You can consider expert help/ training for them if required. Ultimately, it boils down to new managers to win respect and trust of erstwhile peers."

The situation like this is very common and it generally does take time for people to accept change. Here are a few suggestions for your consideration:
a) For each person that you have elevated, set a meeting with his/her team, announce the decision of elevation to the entire team, share the reasons if possible. Share also, what the organization or business unit is looking forward to with this model.
b) If someone tries to bypass the new structure and reach out directly to you, please make sure to involve the supervisor subtly in the discussion/loop.
c) Advise your new supervisors to not to act too differently from days before, ask them to stay friendly, and respect the opinions of their colleagues. They need to drive consensus, build confidence and show humility.
Also suggest them not to get defensive or emotional if this discussion arises in the team.
d) If possible, get a coach to help the supervisors’ transition smoothly.