| 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:
|
http://hdl.handle.net/10338.dmlcz/137444 |
| . |
| Reference:
|
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| Reference:
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| . |
