Some model theory of SL(2;R)

We study the action of G = SL(2;R), viewed as a group denable in the structure M = (R; +; ), on its type space SG(M). We identify a minimal closed G-ow I, and an idempotent r2 I (with respect to the Ellis semigroup structure on SG(M)). We also show that the \ideal group" (r I; ) is nontrivial (in fact it will be the group with 2 elements), yielding a negative answer to a question of Newelski.