Color algebra of three quarks

The color algebra with the outer product ${\mathrm{}[u,v]\mathrm{}}^A=i{f}^{\mathrm{ABC}}(u^B{v}^C+v^C{u}^B)$ is studied for the case of three-quark sources. It is shown to contain two Abelian elements which annihilate the color-singlet state and a sixteen-element ideal which contains an eight-element subalgebra isomorphic to u(2) ⊕ (2). The Jacobi identity is not satisfied on the whole algebra. The quantity that measures the breakdown of the Jacobi identity is calculated.