Pilot reported asymmetric thrust and alternator loss on take off. The Pilot immediately performed an air turn back and precautionary landing at the departure airport.

Narrative

I departed Runway XX. I ran the power up on the brakes until the turbos produced above ambient pressure. I continued the take off roll; and observed all green on the engine pressure and temperature gauges. I passed 80 knots with no problems and continued the take off. When I rotated; I noticed the aircraft wanted to roll hard to the left. I focused on the cranes I had to clear over ZZZ and trimmed out some control pressure. I then noticed the alternator failed. I just flown the aircraft; trimmed it on the previous leg and checked the trims on the pre-flight checklist; therefore I believed there was some asymmetric thrust or drag. Between the Alternator failure and the seeming asymmetric thrust; I believed I may be slowly experiencing an engine problem; or might simply be having multiple systems (Flight Controls and Electrical) have abnormalities at once. As it was very VFR; I advised ATC I would return to ZZZ and complied with their instructions. ZZZ was landing Runway XXR and XXL; so I requested Runway XXL. I landed the aircraft; noticing as I was on final; that I had to substantially reset the Rudder Trim several times. I taxied the aircraft to the ramp; and advised the passengers. I do not know; I suspect their might have been asymmetric thrust.