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Title: Symmetric difference on orthomodular lattices and $Z_2$-valued states (English)
Author: Matoušek, Milan
Author: Pták, Pavel
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 50
Issue: 4
Year: 2009
Pages: 535-547
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: orthomodular lattice
Keyword: quantum logic
Keyword: symmetric difference
Keyword: Boolean algebra
Keyword: group-valued state
MSC: 03G12
MSC: 06A15
MSC: 28E99
MSC: 81P10
idZBL: Zbl 1212.06021
idMR: MR2583131
Date available: 2009-12-22T10:03:19Z
Last updated: 2013-09-22
Stable URL:
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