6 problems

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…

The conjecture. One has

Let $\mathfrak{g}$ be a vector space considered as a Hom-Lie algebra with the zero Hom-Lie structure, and let…

Classification conjecture. If $L$ admits a nontrivial Hom-Lie structure, then $L$ is isomorphic either to a $3$-dimensional simple algebra, or, in the case of positive characterist…

Let $n$ be the dimension parameter, let $G$ be the group indexing the choices of $\sigma$, and let $\mathrm{KW}_{b,\sigma}^{\mathscr{A}}(\xi)$ denote the corresponding arithmetic K…

Lie-algebraicity conjecture. Every such Hom-Lie infinitesimal formal deformation of $\mathfrak{sl}_2(\mathbb{K})$ is actually a Lie algebra.