Loops in Group Theory and Lie Theory (eBook)

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