Reconstructing an atomic orthomodular lattice from the poset of its Boolean sublattices
Quantum Physics
2013-12-06 v2 Logic
Abstract
We show that an atomic orthomodular lattice L can be reconstructed up to isomorphism from the poset B(L) of Boolean subalgebras of L. A motivation comes from quantum theory and the so-called topos approach, where one considers the poset of Boolean sublattices of L=P(H), the projection lattice of the algebra B(H) of bounded operators on Hilbert space.
Keywords
Cite
@article{arxiv.1306.1950,
title = {Reconstructing an atomic orthomodular lattice from the poset of its Boolean sublattices},
author = {Carmen Constantin and Andreas Doering},
journal= {arXiv preprint arXiv:1306.1950},
year = {2013}
}
Comments
12 pages, no figures; v2: minor corrections, improved presentation