Abstract

In this chapter we are going to develop the details of a theory pertaining to Lie Algebras which, although it has its roots in mathematical work of the 1960s (Satake in Ann Math 71:77–110, 1960, [1], Tits in Algebraic Groups and Discontinuous Subgroups, Proceedings of Symposia in Pure Mathematics, Boulder, Colorado, 1965, p. 33–62 [2], Borel, Tits in Groupes reductifs. Publications Mathemathiques de l’IHES 27: 55–151, 1965; Complements a l’article 41:253–276 1972, [3]), contributed by two great algebrists, Jacques Tits and Ichiro Satake (see Fig. 5.1), yet fully revealed its profound significance for Geometry and Physics only much later, by the end of the XXth century, and within the context of supergravity.

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