Local Moufang sets and PSL_2 over a local ring

Abstract

We introduce local Moufang sets as a generalization of Moufang sets. We present a method to construct local Moufang sets from only one root group and one permutation. We use this to describe ${\mathsf{PSL}}_2$ over a local ring as a local Moufang set, and give necessary and sufficient conditions for a local Moufang set to be of this form.

arXiv comment23 pages, fixed a problem in Lemma 5.8, where we need an extra assumption. Other results remain unchanged