Homogeneous spaces and quasigroups
type: Item
instance of: scholarly article
title: Homogeneous spaces and quasigroups
zbMATH Open document ID: 0874.53037
published in: Russian Mathematics
publication date: 1997-10-13T00:00:00Z
review text: The paper is a review dedicated to loops and homogeneous spaces. Let \(G/H\) be a homogeneous space, \(Q\) be a submanifold of the Lie group \(G\) through the unit of \(G\) transversal to the cosets \(gH\). Then we can define a binary operation on \(Q\) by projection on \(Q\) along the leaves \(gH\). Conversely, one can reconstruct a homogeneous space \(G/H\) from the given loop \(Q\). The connection between \(Q\) and \(G/H\) gives a possibility to describe the homogeneous space properties in terms of quasigroup and loop theory.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 22A22
zbMATH DE Number: 1023856
zbMATH Keywords: homogeneous space
zbMATH Keywords: quasigroup
zbMATH Keywords: loop
author: L. V. Sabinin
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1023856