1Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 2School of CEPS University of Central Lancashire Preston, PR1 2HE, UK 3Department of Mathematics University of Notre Dame Notre Dame, IN 46556, U.S.A.
Fundamenta Mathematicae, Tome 229 (2015) no. 2, pp. 117-128
We study the action of $G = {\rm SL} (2,\mathbb R)$, viewed as a group definable in the structure $M = (\mathbb R,+,\times )$, on its type space $S_{G}(M)$. We identify a minimal closed $G$-flow $I$ and an idempotent $r\in I$ (with respect to the Ellis semigroup structure $*$ on $S_{G}(M)$). We also show that the “Ellis group” $(r*I,*)$ is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.
Keywords:
study action mathbb viewed group definable structure mathbb times its type space identify minimal closed g flow idempotent respect ellis semigroup structure * ellis group r*i * nontrivial group elements yielding negative answer question newelski
1
Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2
School of CEPS University of Central Lancashire Preston, PR1 2HE, UK
3
Department of Mathematics University of Notre Dame Notre Dame, IN 46556, U.S.A.
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Jakub Gismatullin; Davide Penazzi; Anand Pillay. Some model theory of ${\rm SL}(2,{\mathbb R})$. Fundamenta Mathematicae, Tome 229 (2015) no. 2, pp. 117-128. doi: 10.4064/fm229-2-2
