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Removing the torsion from a unital group. (English) Zbl 1054.81005
Effect algebras are mathematical structures associated with experimentally testable propositions in quantum mechanics. Most effect algebras that are of interest in applications can be realized as intervals in partially ordered abelian groups. The corresponding group is not uniquely determined, but among all these groups there is a special one, called the unigroup. Every unital group in which \(E\) can be realized is a homomorphic image of the unigroup \(G\) for \(E\). Information about observables, symmetries, and states is encoded in the unigroup \(G\). The “standard” unigroups are all torsion-free. This article pays special attention to the case in which \(G\) is a unital group with a finite unit interval \(E\subseteq G\). (In this case \(G\) is a direct sum of a free abelian group and the torsion subgroup.)

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
06C15 Complemented lattices, orthocomplemented lattices and posets
03G12 Quantum logic
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