Reduced Temperley-Lieb skein theory
= Reduced Temperley-Lieb skein theory
At $A=e^{\pi i/(2r)}$, $r\geq3$, the projector $f_{r-1}$ exists but its closed trace is zero. Quotient by the skein ideal generated by this projector. The surviving simple colors are $0,\ldots,r-2$, with nonzero <quantum dimensions> $d_j=(-1)^j\sin((j+1)\pi/r)/\sin(\pi/r)$. This truncation prevents zero-trace channels from interfering with nondegenerate fusion and surgery normalization.