The lift (A) has a lift drive (4) e.g. reluctance motor, provided with a stator and a rotor. The rotor is connected with a traction sheave. A carrier unit (2) e.g. belt, rests on the traction sheave in a friction-fit manner. The carrier unit is connected with a lift cabin (1) such that a rotary movement of the rotor and the traction sheave moves the lift cabin. The rotor is made of soft magnetic material. The rotor and the traction sheave are connected with each other in a material-fit and/or form-fit and/or force-fit manner. A carrier element is coated with elastomer. An independent claim is also included for a method for operating a lift drive.
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