Orthosymmetries and Jordan triples (Q1266076)

Orthosymmetric weak generalized orthomodular posets (orthosymmetric WGOMPs) are defined. A WGOMP is a certain poset with a smallest element \(0\) such that every interval \([0,a]\) is an orthomodular poset. This generalizes the notion of an orthomodular poset. It is proved that any orthosymmetric WGOMP can be embedded as an order ideal into an orthosymmetric orthoposet. For each Jordan triple the set of all tripotents (idempotents) carries the structure of a WGOMP in some natural way. Connections between WGOMPs and Jordan triples are investigated and some examples are given.