5 problems

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…

The algebra $\mathcal{E}_n$ is generated by braid generators and ties subject to the defining relations, while $\widetilde{\mathcal{E}}_n$ is the corresponding diagram algebra gene…

Let $t_3^0$ be the Markov trace on the specialized algebra described by the conditions $t_3^0(1)=t_3^0(s_1)=0$ and $t_3^0(s_1s_2)=1$. Markov-trace extension conjecture. The trace…

For $n\geq 3$, let $\mathcal{B}_n^{\pm}$ be the specialized algebra, let $\mathcal{I}_n^{\pm}$ be its defining ideal, and let…

Let $d$ and $n$ be positive integers, and let $F_{d,n}$ denote the framization of the Birman–Wenzl–Murakami algebra constructed in the paper. A Markov trace conjecture asserts that…