${\mathrm{SL}}_2$-like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers

Zachary Greenberg, Dani Kaufman, Anna Wienhard

We study $2\times 2$ matrices over noncommutative rings with anti-involution, with a special focus on the symplectic group ${\mathrm{Sp}}_2(\mathcal{A},\sigma )$. We define traces and dete…