Symmetric sets with midpoints and algebraically equivalent theories
type: Item
instance of: scholarly article
title: Symmetric sets with midpoints and algebraically equivalent theories
zbMATH Open document ID: 1066.51006
DOI: 10.1007/BF03322869
author: Yongdo Lim
author: Jimmie D. Lawson
published in: Results in Mathematics
publication date: 2005-02-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20K25
zbMATH DE Number: 2133435
zbMATH Keywords: symmetric space
zbMATH Keywords: symmetric set
zbMATH Keywords: midpoint mean
zbMATH Keywords: idempotent quasigroup
zbMATH Keywords: B-loop
zbMATH Keywords: involutive group
zbMATH Keywords: polar decomposition
reviewed by: Milica Stojanović
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322869
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description: scientific article; zbMATH DE number 2133435