Some Remarks on Kite Pseudo Effect Algebras

TL;DR

This paper introduces kite pseudo effect algebras, a new class of algebraic structures built from po-groups and bijections, characterizing their subdirect products and showing they form intervals in unital po-loops.

Contribution

It provides a characterization of subdirect products of kite pseudo effect algebras and demonstrates that all such algebras are intervals within unital po-loops, expanding understanding of their structure.

Findings

Characterization of subdirect products of kite pseudo effect algebras

Every kite pseudo effect algebra is an interval in a unital po-loop

Kite pseudo effect algebras can be non-commutative even from Abelian po-groups

Abstract

Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group $G$, a set $I$ and with two bijections $\lambda,\rho:I \to I.$ Using a clever construction on the ordinal sum of $(G^+)^I$ and $(G^-)^I,$ we can define a pseudo effect algebra which can be non-commutative even if $G$ is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.