Order automorphisms of effect algebras

TL;DR

This paper provides a simplified proof for the structure of order automorphisms of effect algebras, extending known results to real cases and classifying isomorphisms of matrix intervals.

Contribution

It introduces a simpler proof method using projective geometry and generalizes the classification of order automorphisms to real effect algebras.

Findings

Simplified proof of order automorphisms using projective geometry

Classification of order isomorphisms for matrix intervals

Extension of results to real effect algebras

Abstract

An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application we classify order isomorphic pairs of matrix intervals and describe the general form of order isomorphisms for any pair of isomorphic matrix intervals.