We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on ). 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-2,
author = {Jakub Gismatullin and Davide Penazzi and Anand Pillay},
title = {Some model theory of SL(2,$\mathbb{R}$)},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {117-128},
zbl = {1322.03026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-2}
}
Jakub Gismatullin; Davide Penazzi; Anand Pillay. Some model theory of SL(2,ℝ). Fundamenta Mathematicae, Tome 228 (2015) pp. 117-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-2-2/