Subalgebras of orthomodular lattices

Details Subalgebras of orthomodular lattices Subalgebras of orthomodular lattices

2010-09-22

arxiv.org/abs/1009.4433v1

Physics

Mathematical Physics

13 pages

Scientific paper

Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham, at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional perspective to this line of work.

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