Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

Table of Contents

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