Nikon 1 J1 has a Nikon 1 lens mount and currently there are 13 native lenses available for this mount. Nikon 1 J1 doesn't have a sensor based image stabilization system but 7 of these lenses already comes with optical image stabilization.
Since Nikon 1 J1 has a 1 inch Sensor sensor, it has a focal length multiplier of 2.7× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on 1 J1.
You may also also be interested in these:
Nikon 1 J1 Lenses with Image Stabilization
Nikon 1 J1 Lenses with Weather Sealings