Reconstructing an atomic orthomodular lattice from the poset of its Boolean sublattices
arXiv:1306.1950
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.
12 pages, no figures; v2: minor corrections, improved presentation
References in corpus (6)
- A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
- A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
- A Topos Foundation for Theories of Physics: IV. Categories of Systems
- A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
- Abelian subalgebras and the Jordan structure of a von Neumann algebra
- Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras