3 problems

Let $q=\omega$ be a root of unity of order $N\geq 1$, let $H_{c,t}$ be the $4N$-dimensional Nichols f-algebra with scaling automorphism $\phi_t x_i=t_i x_i$, and let $R_{c,t}$ be t…

Let $S$ be an oriented surface of finite topological type. Suppose that the $d$-root $q^{\frac1d}$ is a root of unity of order $n$ coprime with $2d$, and take the commutative skein…

Let $S$ be an oriented surface of finite topological type. For each puncture, let $[P_i]$ denote the skein represented by a small loop around that puncture with weight…