Loops in Group Theory and Lie Theory

ISBN: 9783110170108 出版年：2011 页码：376 Nagy, Peter Strambach, Karl De Gruyter

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