Resumen de Constructing quaternion and symbol division algebras with given invariants

Péter Kutas

• We propose randomized polynomial time algorithms for constructing quaternion algebras and symbol algebras with prescribed invariants. The key ingredient of these algorithms is an effective function field version of Dirichlet’s theorem on arithmetic progressions. We apply our algorithms to compute primitive idempotents in central simple Fq(t)-algebras given by structure constants.