Geodesic
Some model theory of ${\rm SL}(2,{\mathbb R})$
Jakub Gismatullin1 ; Davide Penazzi2 ; Anand Pillay3
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.
Fundamenta Mathematicae, Tome 229 (2015) no. 2, pp. 117-128 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm229-2-2
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

Jakub Gismatullin 1 ; Davide Penazzi 2 ; Anand Pillay 3

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

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