Advances in Geometry and Lie Algebras from Supergravity

1. Finite Groups and Lie Algebras: The ADE Classification and Beyond
Pietro Giuseppe Fré

2. Isometries and the Geometry of Coset Manifolds
Pietro Giuseppe Fré

3. Complex and Quaternionic Geometry
Pietro Giuseppe Fré

4. Special Geometries
Pietro Giuseppe Fré

5. Solvable Algebras and the Tits Satake Projection
Pietro Giuseppe Fré

6. Black Holes and Nilpotent Orbits
Pietro Giuseppe Fré

7.




$$E_7,



$$F_4 and Supergravity Scalar Potentials
Pietro Giuseppe Fré

8. (Hyper)Kähler Quotients, ALE-Manifolds and



$$mathbb {C}^n/varGamma Singularities
Pietro Giuseppe Fré

9. Epilogue
Pietro Giuseppe Fré

Keywords: Physics, Elementary Particles, Quantum Field Theory, History and Philosophical Foundations of Physics, Differential Geometry, Theoretical, Mathematical and Computational Physics, Mathematical Physics