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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