Overview

In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, toplogical geometry and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for self-study in the subject by interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.

Full Product Details

Author:   Péter Nagy ,  Karl Strambach
Publisher:   De Gruyter
Imprint:   De Gruyter
Edition:   Reprint 2011
Volume:   35
Dimensions:   Width: 17.00cm , Height: 2.20cm , Length: 24.00cm
Weight:   0.760kg
ISBN:  

9783110170108

ISBN 10:   3110170108
Pages:   370
Publication Date:   22 March 2002
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface · Notation · Introduction Part I: General theory of transitive sections in groups and the geometry of loops Elements of the theory of loops · Scheerer extensions of loops · Nets associated with loops · Local 3-nets · Loop-sections covered by 1-parameter subgroups and geodesic loops · Bol loops and symmetric spaces · Bol nets · Strongly topological and analytic Bol loops · Core of a Bol loop and Bruck loops · Bruck loops and symmetric quasigroups over groups · Topological and differentiable Bruck loops · Bruck loops in algebraic groups · Core-related Bol loops · Products and loops as sections in compact Lie groups · Loops on symmetric spaces of groups · Loops with compact translation groups and compact Bol loops · Sharply transitive normal subgroups Part II: Smooth loops on low dimensional manifolds Loops on 1-manifolds · Topological loops on 2-dimensional manifolds · Topological loops on tori · Topological loops on the cylinder and on the plane · The hyperbolic plane loop and its isotopism class · 3-dimensional solvable left translation groups · Classification of differentiable 2-dimensional Bol loops · Collineation groups of 4-dimensional Bol nets · Strongly left alternative plane left A-loops · Loops with Lie group of all translations · Multiplicative loops of quasifields Bibliography

Reviews

""This book is remarkably self-contained, replete with definitions, examples, constructions, and proofs of many of its key results."" Mathematical Reviews ""The present book is a comprehensive treatise devoted to the theory of topological, differentiable and algebraic loops."" Zentralblatt für Mathematik

This book is remarkably self-contained, replete with definitions, examples, constructions, and proofs of many of its key results. Mathematical Reviews The present book is a comprehensive treatise devoted to the theory of topological, differentiable and algebraic loops. Zentralblatt f r Mathematik

This book is remarkably self-contained, replete with definitions, examples, constructions, and proofs of many of its key results. Mathematical Reviews The present book is a comprehensive treatise devoted to the theory of topological, differentiable and algebraic loops. Zentralblatt fur Mathematik

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