Details

Autor(en) / Beteiligte

• Neher, Erhard

Titel

Jordan Triple Systems by the Grid Approach

Ist Teil von

• Lecture Notes in Mathematics : 1280

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1987

Link zum Volltext

• Volltext

Beschreibungen/Notizen

• 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