The Campbell-Hausdorff series of local analytic Bruck loops
type: Item
instance of: scholarly article
title: The Campbell-Hausdorff series of local analytic Bruck loops
zbMATH Open document ID: 1015.20050
DOI: 10.1007/BF02941666
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2003-02-13T00:00:00Z
review text: Moufang and Bol loops are generalizations of the concept of groups. The class of Bruck loops is a subclass of Bol loops. A local Bruck loop is a Bol loop in which a new local multiplication \(x\circ y=(yx^2\cdot y)^{\tfrac 12}\) is defined. \textit{M. A. Akivis} and \textit{V. V. Goldberg} posed the problem of existence of the Campbell-Hausdorff formula for local Bol loops [see Handbook of differential geometry. Vol. 1, 1-152 (2000; Zbl 0968.53001)]. In the paper under review this problem is solved for the class of Bruck loops which is an important subclass of the class of Bol loops.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 53A60
zbMATH DE Number: 1868567
zbMATH Keywords: Bol loops
zbMATH Keywords: local Bruck loops
zbMATH Keywords: Campbell-Hausdorff formula
author: G. P. Nagy
reviewed by: Vladislav V. Goldberg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1868567