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Jordan Triple Systems by the Grid Approach

  • Authors
  • ErhardĀ Neher

Part of the Lecture Notes in Mathematics book series (LNM, volume 1280)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Erhard Neher
    Pages 59-106
  3. Erhard Neher
    Pages 107-135
  4. Erhard Neher
    Pages 136-183
  5. Back Matter
    Pages 184-193

About this book

Introduction

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

Algebra Manifold calculus function functional analysis geometry theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078217
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18362-4
  • Online ISBN 978-3-540-47921-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site