Advances in Geometry and Lie Algebras from Supergravity

Description

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. Front Matter ....Pages i-xx Finite Groups and Lie Algebras: The ADE Classification and Beyond (Pietro Giuseppe Fré)....Pages 1-68 Isometries and the Geometry of Coset Manifolds (Pietro Giuseppe Fré)....Pages 69-98 Complex and Quaternionic Geometry (Pietro Giuseppe Fré)....Pages 99-171 Special Geometries (Pietro Giuseppe Fré)....Pages 173-201 Solvable Algebras and the Tits Satake Projection (Pietro Giuseppe Fré)....Pages 203-263 Black Holes and Nilpotent Orbits (Pietro Giuseppe Fré)....Pages 265-343 \(E_7\), \(F_4\) and Supergravity Scalar Potentials (Pietro Giuseppe Fré)....Pages 345-446 (Hyper)Kähler Quotients, ALE-Manifolds and \(\mathbb {C}^n/\varGamma \) Singularities (Pietro Giuseppe Fré)....Pages 447-551 Epilogue (Pietro Giuseppe Fré)....Pages 553-556