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Analytic quasigroups and geometry. (Analiticheskie kvazigruppy i geometriya.) (Russian) Zbl 0832.22003
Moskva: Izd. Univ. Druzhby Narodov. 109 p. (1991).
The theory of analytic quasigroups and its applications to geometry are the subject of the book under review. This theory is a new branch of mathematics, which is at the juncture of algebra and geometry and which is actively being developed. The content of the book can be seen from the chapter titles: I. Smooth universal algebras. II. Canonical affine connections of loopuscular and odular structures. III. Reductive and symmetric geoodular spaces. IV. \(s\)-spaces. V. Triple Lie algebras. VI. Semidirect product of quasigroups and its transassociant. VII. Differential equations of smooth loops. VIII. Smooth Bol loops. – The results of the book can be applied to nonassociative algebraic structures arising in geometry and other parts of natural science.

MSC:
22A30 Other topological algebraic systems and their representations
53A60 Differential geometry of webs
22-02 Research exposition (monographs, survey articles) pertaining to topological groups
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
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