Symmetric Sets With Midpoints and Algebraically Equivalent Theories
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
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