Loops in Group Theory and Lie Theory
Loops in Group Theory and Lie Theory
复制标题
群论和李理论中的循环
DOI：
10.1515/9783110900583
复制
发表时间：
2002
影响因子：
0.6
通讯作者：
K. Strambach
中科院分区：
文献类型：
--
作者：
P. Nagy;K. Strambach
序言 * 记法 * 导言第一部分：群中传递截面的一般理论和环的几何环理论的元素 * Scheerer扩张的环 * 与环相关的网 * 局部3-网 * 由1-参数子群和测地环覆盖的环截面 * Bol环和对称空间 * Bol网 * 强拓扑和解析Bol环 * Bol环的核和Bruck环 * 群上的Bruck环和对称拟群 * 拓扑和可微Bruck环 * 代数群中的Bruck环 * 与核相关的Bol环 * 作为紧李群中的截面的乘积和环 * 群的对称空间上的环 * 具有紧平移群和紧Bol环的环 * 锐传递正规子群第二部分：低维流形上的光滑环1-流形上的环 * 2维流形上的拓扑环 * 环面上的拓扑环 * 圆柱和平面上的拓扑环 * 双曲平面环及其合痕类 * 3维可解左平移群 * 可微2维Bol环的分类 * 4维Bol网的直射群 * 强左交错平面左A-环 * 具有所有平移的李群的环 * 准域的乘法环
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