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Representation of a unital group having a finite unit interval. (English) Zbl 1074.06007
The paper is a continuation of the author’s previous paper [Rep. Math. Phys. 52, No. 2, 187–203 (2003; Zbl 1054.81005)]. Suppose that we have a unital group with a finite unit interval. Then its state space is a rational polytope. The positive cone satisfies the descending chain condition. If, moreover, the group is torsion-free, then it carries a separating set of states with rational values.

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