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Our SLq(2) extension of the standard model is constructed by replacing theelementary field operators, $\Psi (x)$, of the standard model by$\hat{\Psi}^{j}_{mm'}(x) D^{j}_{mm'}$ where $D^{j}_{mm'}$ is an element of the$2j + 1$ dimensional representation of the SLq(2) algebra, which is also theknot algebra. The allowed quantum states $(j,m,m')$ are restricted by thetopological conditions \begin{equation*} (j,m,m') = \frac{1}{2}(N,w,r+o)\end{equation*} postulated between the states of the quantum knot $(j,m,m')$and the corresponding classical knot $(N,w,r+o)$ where the $(N,w,r)$ are (thenumber of crossings, the writhe, the rotation) of the 2d projection of thecorresponding oriented classical knot. Here $o$ is an odd number that isrequired by the difference in parity between $w$ and $r$. There is also theempirical restriction on the allowed states \begin{equation*}(j,m,m')=3(t,-t_3,-t_0)_L \end{equation*} that holds at the $j=\frac{3}{2}$level, connecting quantum trefoils $(\frac{3}{2},m,m')$ with leptons and quarks$(\frac{1}{2}, -t_3, -t_0)_L$. The so constructed knotted leptons and quarksturn out to be composed of three $j=\frac{1}{2}$ particles which unexpectedlyagree with the preon models of Harrari and Shupe. The $j=0$ particles, beingelectroweak neutral, are dark and plausibly greatly outnumber the quarks andleptons. The SLq(2) or $(j,m,m')$ measure of charge has a direct physicalinterpretation since $2j$ is the total number of preonic charges while $2m$ and$2m'$ are the numbers of writhe and rotation sources of preonic charge. Thetotal SLq(2) charge of a particle, measured by writhe and rotation and composedof preons, sums the signs of the counterclockwise turns $(+1)$ and clockwiseturns $(-1)$ that any energy-momentum current makes in going once around theknot...  Keywords: Quantum group; electroweak; knot models; preon models; dark matter.

On the SLq(2) extension of the standard model and the measure of charge