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Quasigroups, geometry and nonlinear geometric algebra. (English) Zbl 0903.20038
The aim of this paper is to expose the up-to-date methods, ideas and results of a new branch of mathematics that have proved to be useful for applications in physics. Then, a survey of the methods of the theory of quasigroups and loops in algebra and geometry is presented in order to attract the attention of mathematicians and physicists to promising applications of this new branch of mathematics in applied sciences.
MSC:
20N05 Loops, quasigroups
53A60 Differential geometry of webs
53C22 Geodesics in global differential geometry
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