Loops in Group Theory and Lie Theory

By: Karl Strambach, Peter Nagy

Write A Review

Hardcover | 22 March 2002

At a Glance

Hardcover
370 Pages

Age
22

Grade
17

Dimensions(cm)
23.5 x 17.15 x 1.91

Hardcover

$358.64

or 4 interest-free payments of $89.66 with

or

Ships in 5 to 7 business days

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, topological 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 selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.

Industry 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 fuer Mathematik

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Groups & Group Theory

The Art of Gathering

How We Meet and Why It Matters

Paperback

RRP $26.99

$22.99

15%
OFF

The New Psychology of Leadership : 3rd Edition - Identity, Influence and Power - Michael J. Platow

$18.75

The New Psychology of Leadership

2nd Edition - Identity, Influence and Power

Paperback

RRP $97.75

$95.75

The Culture Playbook

60 Highly Effective Actions to Help Your Group Succeed

Paperback

RRP $26.99

$22.99

15%
OFF

Fundamentals of Interviewing and Interrogation - Darrel Lambert

$72.75

11%
OFF

Policing the Crowd

Routledge Advances in Police Practice and Knowledge

Paperback

RRP $69.99

$66.75

Interviewing and Communication in Social Work : Routledge Revivals - Crispin P. Cross

$57.75

Key Topics in Attitudes and Persuasion

BPS Key Topics in Psychology

Hardcover

RRP $305.00

$263.75

14%
OFF

The Social Psychology of Citizenship

Critical Advances and Interdisciplinary Insights

Paperback

RRP $75.99

$71.75

The Social Psychology of Citizenship

Critical Advances and Interdisciplinary Insights

Hardcover

RRP $284.00

$246.75

13%
OFF

Developing Communication and Counselling Skills in Medicine

Routledge Revivals

Hardcover

RRP $179.00

$158.99

11%
OFF

Interpersonal Communication

Putting Theory into Practice

Hardcover

RRP $273.00

$236.99

13%
OFF

Interpersonal Communication

Putting Theory into Practice

Paperback

RRP $158.00

$141.75

10%
OFF

The Psychological After-Effects of Covid : Post-Pandemic Complications and Interventions in India - Uzaina Uzaina

$67.75

11%
OFF

The Psychology of Collective Climate Action

Building Climate Courage

Paperback

RRP $69.99

$62.75

10%
OFF

Preface
Notation
Introduction	p. 1
General theory of transitive sections in groups and the geometry of loops
Elements of the theory of loops	p. 13
Scheerer extensions of loops	p. 42
Nets associated with loops	p. 53
Local 3-nets	p. 60
Loop-sections covered by 1-parameter subgroups and geodesic loops	p. 65
Bol loops and symmetric spaces	p. 80
Bol nets	p. 95
Strongly topological and analytic Bol loops	p. 100
Core of a Bol loop and Bruck loops	p. 102
Bruck loops and symmetric quasigroups over groups	p. 120
Topological and differentiable Bruck loops	p. 129
Bruck loops in algebraic groups	p. 143
Core-related Bol loops	p. 150
Products and loops as sections in compact Lie groups	p. 166
Loops on symmetric spaces of groups	p. 174
Loops with compact translation groups and compact Bol loops	p. 194
Sharply transitive normal subgroups	p. 208
Smooth loops on low dimensional manifolds
Loops on 1-manifolds	p. 235
Topological loops on 2-dimensional manifolds	p. 249
Topological loops on tori	p. 256
Topological loops on the cylinder and on the plane	p. 262
The hyperbolic plane loop and its isotopism class	p. 276
3-dimensional solvable left translation groups	p. 289
4-dimensional left translation group	p. 317
Classification of differentiable 2-dimensional Bol loops	p. 321
Collineation groups of 4-dimensional Bol nets	p. 329
Strongly left alternative plane left A-loops	p. 335
Loops with Lie group of all translations	p. 338
Multiplicative loops of locally compact connected quasifields	p. 344
Bibliography	p. 351
Index	p. 359
Table of Contents provided by Blackwell. All Rights Reserved.

Loops in Group Theory and Lie Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Groups & Group Theory