The Campbell-Hausdorff series of local analytic Bruck loops
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.
scientific article; zbMATH DE number 1868567
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