${\mathrm{SL}}_{\ast }$ over local and adèle rings: $\ast$-euclideanity and Bruhat generators

Luis Gutiérrez Frez, Luis Lomelí, José Pantoja

Let $(R,\ast )$ be a ring with involution and let $A=\mathrm{M}(n,R)$ be the matrix ring endowed with the $\ast$-transpose involution. We study ${\mathrm{SL}}_{\ast }(2,A)$ and the question of Bruhat…