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Automorphisms and symmetries of quantum logics. (English) Zbl 0697.03034
Let L be a quantum logic and let A(L) (S(L),C(L), resp.) denote the group of all automorphisms of L (the group of all symmetries of L, the group of all automorphisms of L which preserve the convex combinations of states, resp.). Then we have natural embeddings i: S(L)\(\to A(L)\) and e: S(L)\(\to C(L)\). Thus, with these embeddings, the triple S(L), A(L) and C(L) forms an amalgam of groups. The author raises the following interesting and highly nontrivial question: Given an amalgam of groups, can we always find its “quantum logic” representation as described above? She proves that we can. She also ensures that the representation enjoys properties significant within quantum theories. The proof she provides uses an advanced graph-theory technique.
Reviewer: P.Ptak

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
20B27 Infinite automorphism groups
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