Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.
The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.
Editorial Board
Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Chapter
2 Scheerer extensions of loops
pp.：
41 – 54
3 Nets associated with loops
pp.：
54 – 65
4 Local 3-nets
pp.：
65 – 72
5 Loop-sections covered by 1-parameter subgroups and geodesic loops
pp.：
72 – 77
6 Bol loops and symmetric spaces
pp.：
77 – 92
8 Strongly topological and analytic Bol loops
pp.：
107 – 112
9 Core of a Bol loop and Bruck loops
pp.：
112 – 114
9.2 Symmetric spaces on differentiable Bol loops
pp.：
114 – 125
9.1 Core of a Bol loop
pp.：
114 – 114
10 Bruck loops and symmetric quasigroups over groups
pp.：
125 – 132
11 Topological and differentiable Bruck loops
pp.：
132 – 141
12 Bruck loops in algebraic groups
pp.：
141 – 155
13 Core-related Bol loops
pp.：
155 – 162
14 Products and loops as sections in compact Lie groups
pp.：
162 – 178
14.2 Crossed direct products
pp.：
178 – 180
14.1 Pseudo-direct products
pp.：
178 – 178
14.3 Non-classical differentiable sections in compact Lie groups
pp.：
180 – 182
14.4 Differentiable local Bol loops as local sections in compact Lie groups
pp.：
182 – 185
15 Loops on symmetric spaces of groups
pp.：
185 – 186
15.2 A fundamental reduction
pp.：
186 – 194
15.1 Basic constructions
pp.：
186 – 186
15.3 Core loops of direct products of groups
pp.：
194 – 198
15.4 Scheerer extensions of groups by core loops
pp.：
198 – 202
16 Loops with compact translation groups and compact Bol loops
pp.：
202 – 206
17 Sharply transitive normal subgroups
pp.：
206 – 220
Part II. Smooth loops on low dimensional manifolds
pp.：
220 – 245
18 Loops on 1-manifolds
pp.：
245 – 247
19 Topological loops on 2-dimensional manifolds
pp.：
247 – 261
20 Topological loops on tori
pp.：
261 – 268
21 Topological loops on the cylinder and on the plane
pp.：
268 – 274
21.2 Non-solvable left translation groups
pp.：
274 – 276
21.1 2-dimensional topological loops on the cylinder
pp.：
274 – 274
22 The hyperbolic plane loop and its isotopism class
pp.：
276 – 288
23 3-dimensional solvable left translation groups
pp.：
288 – 301
23.1 The loops L(α) and their automorphism groups
pp.：
301 – 302
23.2 Sharply transitive sections in £2 × ℝ
pp.：
302 – 310
23.3 Sections in the 3-dimensional non-abelian nilpotent Lie group
pp.：
310 – 320
23.4 Non-existence of strongly left alternative loops
pp.：
320 – 324
24 4-dimensional left translation group
pp.：
324 – 329
25 Classification of differentiable 2-dimensional Bol loops
pp.：
329 – 333
26 Collineation groups of 4-dimensional Bol nets
pp.：
333 – 341
27 Strongly left alternative plane left A-loops
pp.：
341 – 347
28 Loops with Lie group of all translations
pp.：
347 – 350
29 Multiplicative loops of locally compact connected quasifields
pp.：
350 – 356
29.1 2-dimensional locally compact quasifields
pp.：
356 – 357
29.2 Rees algebras Qε
pp.：
357 – 358
29.3 Mutations of classical compact Moufang loops
pp.：
358 – 360
Bibliography
pp.：
360 – 363
Loops in Group Theory and Lie Theory
( De Gruyter Expositions in Mathematics )
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