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Group Theory for Supergravity and Branes Theorists

Pietro Frè - University of Torino, Torino

  Starting with a quick review of the fundamental concepts of Group Theory both finite and continuous the heart of these lectures is centered on the ADE classification of semi-simple Lie Algebras and of finite Kleinian subgroups of SU(2). The basic theory of symmetric spaces is outlined together with the theory of real forms with some highlights on the Tits Satake projection. Next the basic concepts of Kahler Geometry, Special Kahler Geometry, HyperKahler and Quaternionic Kahler manifolds are presented and the c-map and the c-star maps are outlined. Special attention is devoted to (Hyper)-Kahler quotients and the Kronheimer construction of ALE-manifolds is presented with an in depth analysis of the simplest case, namely that of the Eguchi-Hanson metric.  
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