Symmetric sets with midpoints and algebraically equivalent theories
In this paper is considered an algebraic generalization of symmetric spaces of noncompact type to a more general class of symmetric structures equipped with midpoints. These symmetric structures are shown to have close relationships to and even categorical equivalences with a variety of other algebraic structures: axiomatic midpoint spaces, uniquely 2-divisible twisted subgroups, transversal twisted subgroups of involutive groups, a special class of loops called \(B\)-loops, and gyrocommutative gyrogroups.
scientific article; zbMATH DE number 2133435
scientific article