7 problems

Let $A_n(s)$ be the alternating factorization defined in the paper, and let $\widetilde{\operatorname{SL}}(2,\mathbb{R})$ be the universal covering group of…

Let $N$ be a positive integer, let $s_n$ be the switching parameters from the paper, and let $A(N+1;r,s,t)$ be the corresponding alternating factorization. For…

Let $n\in\mathbb{N}$ with $n\geq3$. Let $A_n(s)$ and $A(n;r,s,t)$ denote the alternating factorizations used in the paper, let $s_n$ be the associated switching parameters, and let…

Makhlouf--Silvestrov conjecture. The resulting Hom--Lie algebra $(V,[\cdot,\cdot]_t,\alpha_t)$ is in fact a Lie algebra: the bracket $[\cdot,\cdot]_t$ satisfies the ordinary Jacobi…

Strong-generation conjecture. The subalgebra of $\Pi_{{\rm SL}_2}^{\otimes(s+1)}$ weakly generated by $e_i,h_i,f_i$ for $i=1,\dots,s$ and $X^{++\cdots+}$ is strongly generated by…

Free-field realisation conjecture. The vertex algebra $\mathbf{V}_{{\rm SL}_2,s}$ is isomorphic to the subalgebra of $\Pi_{{\rm SL}_2}^{\otimes(s+1)}$ weakly generated by…

Let $K$ be a $p$-adically closed field and let $H$ be a definable subgroup of $SL_2(K)$. Assume that $H$ is bounded and nonsolvable, and that $w$ does not normalize $H$. Let…