Jordan Structures in Geometry and Analysis

Cover; CAMBRIDGE TRACTS IN MATHEMATICS; Cover; Title; Copyright; Dedication; Contents; Preface; 1 Jordan and Lie theory; 1.1 Jordan algebras; 1.2 Jordan triple systems; 1.3 Lie algebras and the Tits-Kantor-Koecher construction; 1.4 Matrix Lie groups; Notes; 2 Jordan structures in geometry; 2.1 Banach manifolds and Lie groups; 2.2 Riemannian manifolds; 2.3 Jordan algebras and Riemannian symmetric spaces; 2.4 Jordan triples and Riemannian symmetric spaces; 2.5 Jordan triples and symmetric domains; Notes; 3 Jordan structures in analysis; 3.1 Banach spaces; 3.2 Holomorphic mappings.
Presents recent advances of Jordan theory in differential geometry, complex and functional analysis, with numerous examples and historical notes.