Symmetric Sets With Midpoints and Algebraically Equivalent Theories

Authors

Jimmie Lawson, Louisiana State University
Yongdo Lim, Kyungpook National University

Document Type

Article

Publication Date

8-1-2004

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.

Publication Source (Journal or Book title)

Results in Mathematics

First Page

37

Last Page

56

Recommended Citation

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/BF03322869