Smooth Quasigroups and Loops

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