From Surf Wiki (app.surf) — the open knowledge base

Arithmetic Fuchsian group

Quality 0.00 · 0 views · Updated 25 days ago

Arithmetic Fuchsian groups are a special class of Fuchsian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. The prototypical example of an arithmetic Fuchsian group is the modular group P S L 2 ( Z ) {\displaystyle \mathrm {PSL} _{2}(\mathbb {Z} )} . They, and the hyperbolic surface associated to their action on the hyperbolic plane often exhibit particularly regular behaviour among Fuchsian groups and hyperbolic surfaces.