(Ebook) Loops in Group Theory and Lie Theory 1st Edition by Péter Nagy, Karl Strambach ISBN 9783110170108 3110170108

Part I. General theory of transitive sections in groups and the geometry of loops

1 Elements of the theory of loops

1.1 Basic facts on loops

1.2 Loops as sections in groups

1.3 Topological loops and differentiable loops

2 Scheerer extensions of loops

3 Nets associated with loops

4 Local 3-nets

5 Loop-sections covered by 1-parameter subgroups and geodesic loops

6 Bol loops and symmetric spaces

7 Bol nets

8 Strongly topological and analytic Bol loops

9 Core of a Bol loop and Bruck loops

9.1 Core of a Bol loop

9.2 Symmetric spaces on differentiable Bol loops

10 Bruck loops and symmetric quasigroups over groups

11 Topological and differentiable Bruck loops

12 Bruck loops in algebraic groups

13 Core-related Bol loops

14 Products and loops as sections in compact Lie groups

14.1 Pseudo-direct products

14.2 Crossed direct products

14.3 Non-classical differentiable sections in compact Lie groups

14.4 Differentiable local Bol loops as local sections in compact Lie groups

15 Loops on symmetric spaces of groups

15.1 Basic constructions

15.2 A fundamental reduction

15.3 Core loops of direct products of groups

15.4 Scheerer extensions of groups by core loops

16 Loops with compact translation groups and compact Bol loops

17 Sharply transitive normal subgroups

Part II. Smooth loops on low dimensional manifolds

18 Loops on 1-manifolds

19 Topological loops on 2-dimensional manifolds

20 Topological loops on tori

21 Topological loops on the cylinder and on the plane

21.1 2-dimensional topological loops on the cylinder

21.2 Non-solvable left translation groups

22 The hyperbolic plane loop and its isotopism class

23 3-dimensional solvable left translation groups

23.1 The loops L(α) and their automorphism groups

23.2 Sharply transitive sections in £2 × ℝ

23.3 Sections in the 3-dimensional non-abelian nilpotent Lie group

23.4 Non-existence of strongly left alternative loops

24 4-dimensional left translation group

25 Classification of differentiable 2-dimensional Bol loops

26 Collineation groups of 4-dimensional Bol nets

27 Strongly left alternative plane left A-loops

28 Loops with Lie group of all translations

29 Multiplicative loops of locally compact connected quasifields

29.1 2-dimensional locally compact quasifields

29.2 Rees algebras Qε

29.3 Mutations of classical compact Moufang loops

Bibliography

Index