Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

1. Preliminaries
2. Curvature Tensor of an Involutive Pair. Classical Inovolutive Pairs of Index 1
3. Iso-Involutive Sums of Lie Algebras
4. Iso-Involutive Base and Structure Equations
5. Iso-Involutive Sums of Types 1 and 2
6. Iso-Involutive Sums of Lower Index 1
7. Principal Central Involutive Automorphism of Type U
8. Principal Unitary Involutive Automorphism of Index 1
9. Hyper-Involutive Decomposition of a Simple Compact Lie Algebra
10. Some Auxiliary Results
11. Principal Involutive Automorphisms of Type O
12. Fundamental Theorem
13. Principal Di-Unitary Involutive Automorphism
14. Singular Principal Di-Unitary Involutive Automorphism
15. Mono-Unitary Non-Central Principal Involutive Automorphism
16. Exceptional Principal Involutive Automorphism of Types f and e
17. Classification of Simple Special Unitary Subalgebras
18. Hyper-Involutive Reconstructions of Basis Involutive Decompositions
19. Special Hyper-Involutive Sums
20. Notations, Definitions and Some Preliminaries
21. Symmetric Spaces of Rank 1
22. Principal Symmetric Spaces
23. Essentially Special Symmetric Spaces
24. Some Theorems on Simple Compact Lie Groups
25. Tri-Symmetric and Hyper-Tri-Symmetric Spaces
26. Tri-Symmetric Spaces with Exceptional Compact Groups
27. Tri-Symmetric Spaces with Groups of Motions SO(n), Sp(n), SU(n)
28. Subsymmetric Riemannian Homogeneous Spaces
29. Subsymmetric Homogeneous Spaces and Lie Algebras
30. Mirror Subsymmetric Lie Triplets of Riemannian Type
31. Mobile Mirrors. Iso-Involutive Decompositions
32. Homogeneous Riemannian Spaces with Two-Dimensional Mirrors
33. Homogeneous Riemannian Spaces with Groups SO(n), SU(3) and Two-Dimensional Mirrors
34. Homogeneous Riemannian Spaces with Simple Compact Lie Groups of Motions G?SO(n), SU(3) and Two-dimensional Mirrors
35. Homogeneous Riemannian Spaces with Simple Compact Lie Groups of Motions and Two-Dimensional Immobile Mirrors

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Avainsanat: MATHEMATICS / General MAT000000