Symmetric difference on orthomodular lattices and Z 2 -valued states

Milan Matoušek; Pavel Pták

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 4, page 535-547
  • ISSN: 0010-2628

Abstract

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The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of Z 2 -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.

How to cite

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Matoušek, Milan, and Pták, Pavel. "Symmetric difference on orthomodular lattices and $Z_2$-valued states." Commentationes Mathematicae Universitatis Carolinae 50.4 (2009): 535-547. <http://eudml.org/doc/35128>.

@article{Matoušek2009,
abstract = {The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_2$-valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.},
author = {Matoušek, Milan, Pták, Pavel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state; orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state},
language = {eng},
number = {4},
pages = {535-547},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Symmetric difference on orthomodular lattices and $Z_2$-valued states},
url = {http://eudml.org/doc/35128},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Matoušek, Milan
AU - Pták, Pavel
TI - Symmetric difference on orthomodular lattices and $Z_2$-valued states
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 4
SP - 535
EP - 547
AB - The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_2$-valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.
LA - eng
KW - orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state; orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state
UR - http://eudml.org/doc/35128
ER -

References

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