The Structure of an SL2‐module of finite Morley rank

We consider a universe of finite Morley rank and the following definable objects: a field , a non‐trivial action of a group on a connected abelian group V , and a torus T of G such that . We prove that every T‐minimal subgroup of V has Morley rank . Moreover V is a direct sum of ‐minimal subgroups of the form , where W is T‐minimal and ζ is an element of G of order 4 inverting T .