On the self-similarity of the norm one group of $p$-adic division algebras

Francesco Noseda, Ilir Snopce

Let $p$ be a prime, $D$ a finite dimensional noncommutative division ${\mathbb{Q}}_p$-algebra, and $S{L}_1(D)$ the group of elements of $D$ of reduced norm $1$. When the center of $D$…