Would you expect to see auroras on the moon?

No, you would not expect to see auroras on the Moon as you do on Earth. Auroras are caused by interactions between the solar wind and a planet's magnetic field and atmosphere, which the Moon lacks. While the Moon does have a very thin exosphere, it does not possess a significant magnetic field to create the conditions necessary for auroras. Therefore, any potential auroral phenomena on the Moon would be vastly different and much less visible than those on Earth.