40 arranged in the leaf are in contact with a runner rail 42 arranged on the frame when the door leaf 16 is lowered the door leaf 16 lies with an underside 44 on the runner rail 42 the second vertical profile section 28 serves for arranging components of a drive device 46 described below for displacing the door leaf 16 in the horizontal direction a drive motor 48 the drive axis 50 of which is oriented in the vertical direction is arranged in an upper region of the second vertical profile section 28 the drive motor 48 cooperates with an output stage 52 which is preferably arranged beneath the drive motor 48 in the second vertical profile section 28 an output stage 54 which cooperates with the motor driven lifting device 38 is preferably arranged on a lower end of the second vertical profile section 28 furthermore the second vertical profile section 28 serves for arranging a controller 56 and also at least one battery 58 60 in the schematic view of fig1 lines between the described components of the sliding door assembly 10 are illustrated with unbroken or dotted lines in this case the unbroken lines represent current conducting lines while the dotted lines represent data lines the lines mentioned likewise run within the profile sections 22 24 26 and 28 of the door leaf 16 however in order to improve clarity in fig1 the lines are illustrated as if they run through the panel 20 the drive motor 48 has an output shaft 62 which cooperates in positive manner with a shaft 64 illustrated in fig2 the shaft 64 is connected for conjoint rotation with a gear wheel 66 the gear wheel.