Description: 0. Introductory Survey: Quasigroups, Loopuscular Geometry and Nonlinear Geometric Algebra.- One. Fundamental Structures of Nonlinear Geometric Algebra.- 1. Basic Algebraic Structures.- 2. Semidirect Products of a Quasigroup by its Transassociants.- 3. Basic Smooth Structures.- Two. Smooth Loops and Hyperalgebras.- 4. Infinitesimal Theory of Smooth Loops.- 5. Smooth Bol Loops and Bol Algebras.- 6. Smooth Moufang Loops and Mal'cev Algebras.- 7. Smooth Hyporeductive and Pseudoreductive Loops.- Three. Loopuscular Geometry.- 8. Affine Connections and Loopuscular Structures.- 9. Reductive Geoodular Spaces.- 10. Symmetric Geoodular Spaces.- 11. s-SPACES.- 12. Geometry of Smooth Bol And Moufang Loops.- Appendices.- Appendix 1. Lie Triple Algebras and Reductive Spaces.- Appendix 2. Left F-Quasigroups. Loopuscular Approach.- Appendix 3. Left F-Quasigroups and Reductive Spaces.- Appendix 4. Geometry of Transsymmetric Spaces.- Appendix 5. Half Bol Loops.- Appendix 6. Almost Symmetric and Antisymmetric Manifolds.- Appendix 7. Right Alternative Local Analytic Loops.

Please Wait