TY  - BOOK
AU  - Neher,Erhard
ED  - SpringerLink (Online service)
TI  - Jordan Triple Systems by the Grid Approach
T2  - Lecture Notes in Mathematics,
SN  - 9783540479215
AV  - QA150-272 
U1  - 512 23
PY  - 1987///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Algebra
N1  - Special families of compatible tripotents -- Classification of grids -- Coordinatization theorems -- Classifications
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0078217
ER  -