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L-mosaics and orthomodular lattices

Nicolò Cangiotti, Alessandro Linzi, Enrico Talotti

Abstract

In this paper, we introduce a class of hypercompositional structures called dualizable L-mosaics. We prove that their category is equivalent to that formed by ortholattices and we formulate an algebraic property characterizing orthomodularity, suggesting possible applications to quantum logic.

L-mosaics and orthomodular lattices

Abstract

In this paper, we introduce a class of hypercompositional structures called dualizable L-mosaics. We prove that their category is equivalent to that formed by ortholattices and we formulate an algebraic property characterizing orthomodularity, suggesting possible applications to quantum logic.
Paper Structure (12 sections, 52 theorems, 88 equations, 2 figures, 6 tables)

This paper contains 12 sections, 52 theorems, 88 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Mosaics
  3. Orthomodular lattices
  4. Nakano mosaics
  5. Orthomodularity and Nakano mosaics
  6. Further research: the connection with the quantum world
  7. Introduction
  8. Mosaics
  9. Orthomodular lattices
  10. Nakano mosaics
  11. Orthomodularity and Nakano mosaics
  12. Further research: the connection with the quantum world

Key Result

Lemma 2.6

Let $(A,\boxdot,e,\rho)$ be a mosaic. Then $\rho$ is a unitary isomorphism of magmata satisfying the following property: In addition, the equivalences hold for all $x,y,z\in A$.

Figures (2)

  • Figure :
  • Figure :

Theorems & Definitions (132)

  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5: NR23
  • Lemma 2.6: NR23
  • proof
  • Definition 2.7
  • Corollary 2.8
  • Lemma 2.9
  • ...and 122 more