3 problems

Let $B_5$ be the braid group on five strands, let $Q(x)=x^3-\alpha x^2-\beta x-1$, and let … be the corresponding cubic Hecke algebra. The algebra $G_{32}$ is the finite group asso…

Let $Q(x)=x^3-\alpha x^2-\beta x-1$, and let $H(Q,n)=\mathbb{C}[B_n]/(Q(b_j);\,j=1,\dots,n-1)$ be the cubic Hecke algebra. The invariant $I_{(\alpha,\beta)}$ is defined by a Markov…

Let $b1\in\mathbb{C}\setminus\mathbb{Q}$, let $H_n(\alpha)$ be the cubic Hecke algebra through which the braid-group representation factors, and let $r_2$ and $r_3$ be the relation…