Jordan Triple Systems by the Grid Approach [electronic resource] / by Erhard Neher.
Material type: TextSeries: Lecture Notes in Mathematics ; 1280Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1987Description: XIV, 194 p. online resourceContent type:- text
- computer
- online resource
- 9783540479215
- 516.35 23
- QA564-609
Special families of compatible tripotents -- Classification of grids -- Coordinatization theorems -- Classifications.
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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