2021/07/11 by Bao, Jiaqi, Yao, Ningyuan
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2107.04963
We study the p-adic algebraic groups G from the definable topological-dynamical point of view. We consider the case that M is an arbitrary p-adic closed field and G an algebraic group over \mathbb Qp admitting an Iwasawa decompostion G=KB, where K is open and definably compact over \mathbb Qp, and B is a borel subgroup of G over \mathbb Qp. Our main result is an explicit description of the minimal subflow and Ellis Group of the universal definable G(M)-flow SG(Mext). We prove that the Ellis group of SG(Mext) is isomorphic to the Ellis group of SB(Mext), which is B/B0. As applications, we conclude that the Ellis groups corresponding to GL(n,M) and SL(n,M) are isomorphic to ( \mathbb Z × \mathbb Zp^*)n and ( \mathbb Z × \mathbb Zp^*)n-1 respectively, generalizing the main result of Penazzi, Pillay, and Yao in Some model theory and topological dynamics of p-adic algebraic groups, Fundamenta Mathematicae, 247 (2019), pp. 191--216.