In quantum field theory, we use the universal cover of the Lorentz group SL(2,C) instead of SO(3,1). (The reason for this is, of course, that representations of SO(3,1) aren't able to describe spin 1/2 particles.) How is the invariant speed of light enocded in SL(2,C)? This curious fact of nature, is encoded in SO(3,1), because this is exactly the group that leaves the Minkowski metric invariant. In contrast, SL(2,C) is just the group of complex 2x2 matrices with unit determinant.