Subgroups of 𝑆𝐿₂(ℤ) characterized by certain continued fraction representations
Sandie Han, Ariane Masuda, Satyanand Singh, Johann Thiel · Proceedings of the American Mathematical Society · 2020
For positive integers u u and v v , let L u = [ 1 a m p ; 0 u a m p ; 1 ] L_u=\left [\begin {smallmatrix} 1 & 0 \\ u & 1 \end {smallmatrix}\right ] and R v = [ 1 a m p ; v 0 a m p ; 1 ] R_v=\left [\begin {smallmatrix} 1 & v \\ 0 & 1 \end {smallmatrix}\right ] . Let S u , v S_{u,v} be the monoid generated by L u L_u and R v R_v , and let G u , v G_{u,v} be the group generated by L u L_u and