11 problems

For each $n$, let $QA_n$ be the quadratic algebra generated by the cohomology classes associated with the generators of the quasitriangular group, and let…

For each $n$, let ${\mathfrak{qtr}}_n$ be the Lie algebra generated by the elements $r_{ij}$, subject to the classical Yang–Baxter relations, and let ${\mathbf{QTr}}_n$ be the grou…

Let $R_{\text{GGS}}$ be the matrix defined by … where the polynomials $P_{i,j,k,l}$ are uniquely determined by … Here $q=e^{\hbar}$, and the quantum Yang–Baxter equation is … while…

Level-two homology formula conjecture.

Free-rank conjecture. The rank of the free part of $H_n(R_{(m)})$ is $2^{m-1}$ for $n\geq m-1$, while

Let $[? Let$[?

Let $N\in\mathbb{N}$, let $(1,R)\in YB^1(\mathsf{Match}^N)$, and let $X$ be a diagonal matrix in $\mathsf{Mat}^N(2,2)$. Define … For each $n$, let $\rho_n^R$ and $\rho_n^S$ denote…

The even part of the Haagerup subfactor planar algebra $H\mathcal{P}$ is a subfactor planar algebra lying in a one-parameter family of subfactor planar algebras. Haagerup family co…

Let $\lambda$ be an arbitrary weight and let $\Gamma$ be a reduced chain of roots corresponding to $\lambda$. Write $\mathcal{A}(\Gamma)$ for the associated quantum alcove model, a…

Let $G$ be a non-trivial finite group, let $\cP_\bullet$ be a $3^G$ subfactor planar algebra, and let $\cR_\bullet$ be its reduced subfactor planar algebra. A Yang–Baxter planar al…

Let $(V,c)$ be a group-type BVS, and let $G=\langle g_i\rangle$ be the group generated by its associated operators. Assume that $c$ is unitary and has finite order. Finite-group or…