Loops in Group Theory and Lie Theory

Prof. Dr. Karl Strambach ist seit 1972 ordentlicher Professor an der Universität Erlangen. Nach seiner Habilitation arbeitete er zunächst als Universitätsdozent und Wissenschaftlicher Rat an der Universität Tübingen sowie als Professor an der Universität Kiel. 2007 wurde ihm vonder Universität Debrecen die Ehrendoktorwürde verliehen.

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

"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