Overview

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.

Full Product Details

Author:   L. Sabinin
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   492
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.230kg
ISBN:  

9780792359203

ISBN 10:   0792359208
Pages:   249
Publication Date:   31 August 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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