This is a joint project by Oliver Braun, Renaud Coulangeon, Gabriele Nebe and Sebastian Schönnenbeck. The database contains generators and presentations of the unit groups of certain orders in various types of simple rational algebras of small degree.

Database: Unit Groups of Orders

• Quaternion algebras over imaginary quadratic number fields
• Indefinite quaternion algebras over the rationals
• Matrix rings over imaginary quadratic number fields
• Rational division algebras of degree 3

• Quaternion algebras over imaginary quadratic number fields
• Indefinite quaternion algebras over the rationals
• Rational division algebras of degree 3
• S-arithmetic subgroups of exceptional groups