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Smooth Quasigroups and Loops : Mathematics and Its Applications - Lev Sabinin

Smooth Quasigroups and Loops

Mathematics and Its Applications

Hardcover Published: 31st August 1999
ISBN: 9780792359203
Number Of Pages: 249

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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 Lie-group 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.

Preface
Introduction
Introductory Survey: Quasigroups, Loopuscular Geometry and Nonlinear Geometric Algebrap. 1
Fundamental Structures of Nonlinear Geometric Algebrap. 21
Basic Algebraic Structuresp. 23
Semidirect Products of a Quasigroup by Its Transassociantsp. 36
Basic Smooth Structuresp. 47
Smooth Loops and Hyperalgebrasp. 57
Infinitesimal Theory of Smooth Loopsp. 59
Smooth Bol Loops and Bol Algebrasp. 87
Smooth Moufang Loops and Mal'cev Algebrasp. 105
Smooth Hyporeductive and Pseudoreductive Loopsp. 111
Loopuscular Geometryp. 129
Affine Connections and Loopuscular Structuresp. 131
Reductive Geoodular Spacesp. 146
Symmetric Geoodular Spacesp. 155
s-Spacesp. 166
Geometry of Smooth Bol and Moufang Loopsp. 175
Appendicesp. 183
Lie Triple Algebras and Reductive Spacesp. 185
Left F-Quasigroups. Loopuscular Approachp. 189
Left F-Quasigroups and Reductive Spacesp. 199
Geometry of Transsymmetric Spacesp. 205
Half Bol Loopsp. 210
Almost Symmetric and Antisymmetric Manifoldsp. 218
Right Alternative Local Analytic Loopsp. 226
Bibliographyp. 229
Indexp. 245
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792359203
ISBN-10: 0792359208
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 249
Published: 31st August 1999
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.56

Earn 317 Qantas Points
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