Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit

In this article, we prove that the compact simple Lie groups $\mathrm{S}\mathrm{U}(n)$ for $n\ge 6$, $\mathrm{S}\mathrm{O}(n)$ for $n\ge 7$, $\mathrm{S}\mathrm{p}(n)$ for $n\ge 3$, ${\mathrm{E}}_6,{\mathrm{E}}_7,{\mathrm{E}}_8$, and ${\mathrm{F}}_4$ admit left-invariant Einstein metrics that are not geodesic orbit. This gives a positive answer to an open problem recently posed by Nikonorov.     

Ideals in deformation quantizations over Z/pnZ

Let k be a perfect field of characteristic $p>2$. Let $A_1$ be an Azumaya algebra over a smooth symplectic affine variety over k. Let $A_n$ be a deformation quantization of $A_1$ over $W_n(\mathbf{k})$. We prove that all $W_n(\mathbf{k})$-flat two-sided ideals of $A_n$ are generated by central elements.