Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

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ISBN: 978-1-4020-2544-0 (Print) 978-1-4020-2545-7 (Online)

Table of contents (35 chapters)

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  1. Part One

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      Book Chapter

      Pages 3-8

      Preliminaries

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      Book Chapter

      Pages 9-11

      Curvature Tensor of an Involutive Pair. Classical Inovolutive Pairs of Index 1

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      Book Chapter

      Pages 12-15

      Iso-Involutive Sums of Lie Algebras

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      Book Chapter

      Pages 16-27

      Iso-Involutive Base and Structure Equations

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      Book Chapter

      Pages 28-33

      Iso-Involutive Sums of Types 1 and 2

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      Book Chapter

      Pages 34-44

      Iso-Involutive Sums of Lower Index 1

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      Book Chapter

      Pages 45-45

      Principal Central Involutive Automorphism of Type U

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      Book Chapter

      Pages 46-48

      Principal Unitary Involutive Automorphism of Index 1

  2. Part Two

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      Book Chapter

      Pages 51-56

      Hyper-Involutive Decomposition of a Simple Compact Lie Algebra

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      Book Chapter

      Pages 57-59

      Some Auxiliary Results

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      Book Chapter

      Pages 60-68

      Principal Involutive Automorphisms of Type O

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      Book Chapter

      Pages 69-76

      Fundamental Theorem

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      Book Chapter

      Pages 77-86

      Principal Di-Unitary Involutive Automorphism

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      Book Chapter

      Pages 87-94

      Singular Principal Di-Unitary Involutive Automorphism

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      Book Chapter

      Pages 95-102

      Mono-Unitary Non-Central Principal Involutive Automorphism

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      Book Chapter

      Pages 103-110

      Exceptional Principal Involutive Automorphism of Types f and e

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      Book Chapter

      Pages 111-116

      Classification of Simple Special Unitary Subalgebras

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      Book Chapter

      Pages 117-124

      Hyper-Involutive Reconstructions of Basis Involutive Decompositions

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      Book Chapter

      Pages 125-140

      Special Hyper-Involutive Sums

  3. Part Three

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      Book Chapter

      Pages 143-147

      Notations, Definitions and Some Preliminaries

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