This monograph presents the complete theory of smooth quasigroups and loops, as well as its geometric and algebraic applications. Based on a generalisation of the Liegroup theory, it establishes new backgrounds for differential geometry in the form of nonlinear geometric algebra and `loopuscular' geometry. It will prove useful in applications in such diverse fields as mathematical physics, relativity, Poisson and symplectic mechanics, quantum gravity, dislocation theory, etc. Audience: This volume will be of interest to researchers, lecturers and postgraduate students whose work involves geometry, group theory, nonassociative rings and algebras, and mathematical and theoretical physics.

Authors: Sabinin L.V.  Pages: 257 Year: 1999 
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