Differential equations of geometric odule
type: Item
instance of: scholarly article
title: Differential equations of geometric odule
zbMATH Open document ID: 0890.53023
published in: Doklady Mathematics
publication date: 1998-06-25T00:00:00Z
review text: By definition, a geometric odule is a left loop \(M(\cdot)\) such that (1) power associativity law holds in \(M\) and (2) the operator \(x\to x^t\) commutes with the operators \(L^{-1}_{a\cdot b}\circ L_a\circ L_b\), where \(L_a(x)=a\cdot x\). Differential equations of a geometric odule are found and it is proved that any geometric odule is a geodesic one for some affine connection.
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 1050510
zbMATH Keywords: analytic loop
zbMATH Keywords: geometric odule
zbMATH Keywords: affine connection
author: L. V. Sabinin
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
Recommended article: Geometry of differential equations
Recommended article: Q4488494
Recommended article: Q4398580
Recommended article: Q3320498
Recommended article: Differential geometry from differential equations
Recommended article: The geometry of differential difference equations
Recommended article: Geometric properties of solutions of a class of differential equations
Recommended article: Geometric linearization of ordinary differential equations
Recommended article: Q5688871
description: scientific article; zbMATH DE number 1050510