4 problems

Braided tangent-field conjecture. Equations (4) hold if we replace $U_i$ by $U_i^q$ and $f_{\beta,i}$ by $f_{\beta,i}(q)$.

Let ${\cal L}(q)$ be the algebra associated with a Hecke symmetry of the form … fstarq g=fg+nu c1(f,g)+nu^2c2(f,g)+cdots,qquad nu=log(q). … {sigma^{m,n}}(ci(f,g)otimes h)=(Iotimes…

Let ${\rm Tr}_R L^k\in {\cal L}^k(R)$ be the braided trace power, and let $P_+^{(k)}$ and $P_{+2}^{(k-1)}$ be the symmetrizer operators acting on the corresponding tensor powers. P…

Canonical q-symmetrized form conjecture. Any element $f\in{\cal L}(R_q)$ or $f\in{\cal SL}(R_q)$ has a canonical, that is, completely $q$-symmetrized, form.