Symmetric sets with midpoints and algebraically equivalent theories
In this paper we consider an algebraic generalization of symmetric spaces of noncom pact 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-Ioops, and gyrocommutative gyrogroups.
Publication Source (Journal or Book title)
Results in Mathematics
Lawson, J., & Lim, Y. (2004). Symmetric sets with midpoints and algebraically equivalent theories. Results in Mathematics, 46 (1-2), 37-56. https://doi.org/10.1007/s00025-004-0129-x