Chain spaces with many reflections
Let \(\Sigma=({\mathbf P},{\mathcal C})\) be a chain space, where \({\mathbf P}\) is a set of points and \({\mathcal C}\) is a set of chains. Let \(\Pi\) be a subgroup of the automorphism group \(\text{ Aut} \Sigma\) and let \(I\) be a distinguished set of involutions in \(\Pi;\) the elements in \(I\) are called reflections. The author gives axioms for chain spaces, one of the axioms is the three-reflection theorem. She obtains coordinatizations for certain chain spaces with reflections, i.e., she determines \(\Pi',\) \(K,\) \(R\) such that \((\Pi,\Sigma)\cong(\Pi',\Sigma(K,R)),\) where \(K\) is a field, \(R\) is a commutative stable \(K\)-algebra, and \(\Pi'\leq PGL_2(R).\)
scientific article; zbMATH DE number 1760622