All examples of lorentz invariant quantities that I have come across seem to be scalars: rest mass, proper time, spacetime interval,dot product of two 4 vectors etc. Another thing is that these are all index contractions.
So, is there any lorentz invariant quantity which isn't a Lorentz scalar?
(My guess is that there isn't: if the quantity isn't scalar, it must have indices. Such a thing must be a tensor of non zero rank. But a thing which is a tensor under lorentz transformation will have its components change from frame to frame and therefore can't be an invariant. One loophole in this reasoning is to assume that the indexed quantity is in fact a tensor of some rank. So, is it possible to have indexed quantities constructed from spacetime which aren't tensors? )