Abstract
We study definable topological dynamics of some algebraic group actions over an arbitrary NIP field K. We show that the Ellis group of the universal definable flow of SL2(K) is non-trivial if the multiplicative group of K is not type-definably connected, providing a way to find multiple counterexamples to the (model-theoretic) Ellis group conjecture, particularly in the case of dp-minimal fields. We also study some structure theory of algebraic groups over K with definable f-generics.
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