Abstract
In this paper we consider 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.
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Lawson, J., Lim, Y. Symmetric Sets With Midpoints and Algebraically Equivalent Theories. Results. Math. 46, 37–56 (2004). https://doi.org/10.1007/BF03322869
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DOI: https://doi.org/10.1007/BF03322869