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The Structure Group of a Generalized Orthomodular Lattice

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Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.

Jacques Hadamard

Abstract

Orthomodular lattices with a two-valued Jauch–Piron state split into a generalized orthomodular lattice (GOML) and its dual. GOMLs are characterized as a class of L-algebras, a quantum structure which arises in the theory of Garside groups, algebraic logic, and in connections with solutions of the quantum Yang–Baxter equation. It is proved that every GOML X embeds into a group G(X) with a lattice structure such that the right multiplications in G(X) are lattice automorphisms. Up to isomorphism, X is uniquely determined by G(X), and the embedding \(X\hookrightarrow G(X)\) is a universal group-valued measure on X.

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Authors and Affiliations

  1. Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    Wolfgang Rump

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  1. Wolfgang Rump
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Correspondence to Wolfgang Rump.

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Dedicated to B. V. M.

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Rump, W. The Structure Group of a Generalized Orthomodular Lattice. Stud Logica 106, 85–100 (2018). https://doi.org/10.1007/s11225-017-9726-z

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  • DOI: https://doi.org/10.1007/s11225-017-9726-z

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