Jordan Triple Systems by the Grid Approach

Erhard Neher (auth.)9780387183626, 0-387-18362-0

Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are – classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs – a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface – structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

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Table of contents :
Special families of compatible tripotents….Pages 1-58
Classification of grids….Pages 59-106
Coordinatization theorems….Pages 107-135
Classifications….Pages 136-183