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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.

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1 Finite Groups and Lie Algebras

2 Isometries and the Geometry of COSET Manifolds

3 Complex and Quaternionic Geometry

4 Special Geometries

5 Solvable Algebras and the TITS Satake Projection

6 Black Holes and Nilpotent Orbits

7 E7, F4 and supergravitiy scalar potentials

8 (Hyper)Kaehler Quotients, Ale-Manifolds and Cn/ Singularities

9 Epilogue

10 The Bibliography

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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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