Nagy, Peter T., Strambach, K. 　著

内容

目次

Part 1 General theory of transitive sections in groups and the geometryof loops: elements of the theory of loops; Scheerer extensions of loops; netsassociated with loops; local 3-nets; loop-sections covered by 1-parametersubgroups and geodesic loops; Bol loops and symmetric spaces; Bol nets;strongly topological and analytic Bol loops; core of a Bol loop and Bruckloops; Bruck loops and symmetric quasigroups over groups; topological anddifferentiable Bruck loops; Bruck loops in algebraic groups; core-related Bolloops; products and loops as sections in compact Lie groups; loops onsymmetric spaces of groups; loops with compact translation groups and compactBol loops; sharply transitive normal subgroups. Part 2 Smooth loops on lowdimensional manifolds: loops on 1-manifolds; topological loops on2-dimensional manifolds; topological loops on tori; topological loops on thecylinder and on the plane; the hyperbolic plant loop and its isotopism class;3-dimensional solvable left translation groups; classification ofdifferentiable 2-dimensional Bol Loops; collineation groups of 4-dimensionalBol nets; strongly left alternative plane left A-Loops; loops with Lie groupof all translations; multiplicative loops of quasifields.