what are they?
There are three quarks (with three color indices i=1,2,3); this can be written as qi. Now we want to introduce an algebra of matrices A acting on this object qi, that means Aik qk (with a sum over k). These matrices A live in a 3*3 matrix algebra. For complex qi there are two possibilities u(3) and su(3). u(3) is something like u(1) + su(3) which means that there would be a structure like u(1) which corresponds to a long-range force w/o self-interaction which is something like electromagnetism. b/c we do not observe this force we have to chose su(3) instead. Writing down basis vectors for this su(3) algebra one finds that there are eight, not nine, b/c due to the 's' in 'su(3)' one must use only traceless matrices; a matrix with trace ≠ 0 would correspond to the u(1). This reduces the nine possible basis vectors to eight.
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