quantum chromodynamics - Mathematically, what is color charge?

A similar question was asked here, but the answer didn't address the following, at least not in a way that I could understand.

Electric charge is simple - it's just a real scalar quantity. Ignoring units and possible quantization, you could write $q \in \mathbb{R}$. Combination of electric charges is just arithmetic addition: $q_{net} = q_1 + q_2$.

Now to color charge. Because there are three "components", I am tempted to conclude that color charges are members of $\mathbb{R}^3$. However, I've read that "red plus green plus blue equals colorless", which seems to rule out this idea. I can only think that either:

• red, green and blue are not orthogonal, or


• "colorless" doesn't mean zero color charge (unlikely), or


• color charges don't combine in a simple way like vector addition

In formulating an answer, please consider that I know some mathematics (vectors, matrices, complex numbers, calculus) but almost nothing about symmetry groups or Lie algebras.