Jordan Structures in Geometry and Analysis

Jordan Structures in Geometry and Analysis

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Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Titsa€“Kantora€“Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.where 1Z1 = 11Balt;a. a)a#39;/a#39;gL, (a)(z)|| 5 11B(a. a)a#39;/211 11gL.alt;aagt;alt;zagt;11 gives . alt;1- llall)||z|l aquot;f W1)aquot; Z alt;1+11o11agt;11Balt;a.o)1/111a#39; m We conclude this section with a brief discussion of the dynamics of a holomorphic map, namely, the behavior of theanbsp;...

Title:Jordan Structures in Geometry and Analysis
Author: Cho-Ho Chu
Publisher:Cambridge University Press - 2011-11-17

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