Advances in Geometry and Lie Algebras from Supergravity

1. Front Matter

   Pages i-xx

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2. Finite Groups and Lie Algebras: The ADE Classification and Beyond

   • Pietro Giuseppe Fré

   Pages 1-68

3. Isometries and the Geometry of Coset Manifolds

   • Pietro Giuseppe Fré

   Pages 69-98

4. Complex and Quaternionic Geometry

   • Pietro Giuseppe Fré

   Pages 99-171

5. Special Geometries

   • Pietro Giuseppe Fré

   Pages 173-201

6. Solvable Algebras and the Tits Satake Projection

   • Pietro Giuseppe Fré

   Pages 203-263

7. Black Holes and Nilpotent Orbits

   • Pietro Giuseppe Fré

   Pages 265-343

8. \(E_7\), \(F_4\) and Supergravity Scalar Potentials

   • Pietro Giuseppe Fré

   Pages 345-446

9. (Hyper)Kähler Quotients, ALE-Manifolds and \(\mathbb {C}^n/\varGamma \) Singularities

   • Pietro Giuseppe Fré

   Pages 447-551

10. Epilogue

    • Pietro Giuseppe Fré

    Pages 553-556

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity.

The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject. 

• Supersymmetry/supergravity.
• Group theory for physicists
• Lie groups
• Special geometries
• Black holes
• Geometry of symmetric spaces
• Strings and branes
• Differential geometry of Coset manifolds
• quaternionic geometry
• Kaehler quotient
• ale manifolds
• nilpotent orbits
• Tits-Satake projection

Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. He has taught General Relativity for 15 years. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously published four scientific monographs. He is also the author of a popular science book on cosmology (“Il fascino oscuro dell’inflazione”, Springer 2009), and two novels, in Italian.

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