Derived arithmetic Fuchsian groups of genus two. (English) Zbl 1184.11015

Macasieb, Melissa L.

Exp. Math. 17, No. 3, 347-369 (2008).

The author classifies all cocompact torsion-free derived arithmetic Fuchsian groups of genus two by commensurability classes and shows that there exist no such groups arising from quaternion algebras over number fields of degree greater than five. Also, she proves some results on the existence and form of maximal orders for a class of quaternion algebras related to these groups.

Reviewer: Osman Bizim (Bursa)

MSC:

11F06	Structure of modular groups and generalizations; arithmetic groups
11R52	Quaternion and other division algebras: arithmetic, zeta functions
20H10	Fuchsian groups and their generalizations (group-theoretic aspects)
57M50	General geometric structures on low-dimensional manifolds

Keywords:

hyperbolic orbifolds; arithmetic Fuchsian groups; maximal orders