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.

Keywords

Bibliographic Information

Book Title: Jordan Triple Systems by the Grid Approach
Authors: Erhard Neher
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0078217
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1987
Softcover ISBN: 978-3-540-18362-4Published: 16 September 1987
eBook ISBN: 978-3-540-47921-5Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 194
Topics: Algebraic Geometry, Algebra

Publish with us

Policies and ethics

Authors:

Sections

Buy it now

Buying options

Other ways to access

Table of contents (4 chapters)

Front Matter

Special families of compatible tripotents

Classification of grids

Coordinatization theorems

Classifications

Back Matter

About this book