Groups of Small Typical Differential Dimension

We apply techniques from ω-stable and superstable groups to strongly connected and almost simple differential algebraic groups in the sense of Cassidy and Singer. We analyze differential algebraic group actions from this point of view, and prove several results regarding interpreting fields from these actions. We prove a differential algebraic analogue of Rienecke’s theorem. We show that every strongly connected differential algebraic group with typical differential dimension two is solvable. A special instance of the Cassidy-Singer conjecture is confirmed. Namely, noncommutative almost simple groups of typical differential dimension 3 are equal to SL2(F ) or PSL2(F ) for a definable subfield F.