正交模格的子代数
Subalgebras of orthomodular lattices
摘要：
萨克斯证明了一个布尔代数是由它的子代数格决定的。我们建立了正交模格的相应结果。证明了正交模格L由其子代数Sub（L）的格和布尔子代数BSub（L）的偏序集决定。域BSub（L）最近在巴特菲尔德和伊沙姆发起的量子力学基础的方法中找到了用途，至少在L是希尔伯特空间或冯诺依曼代数的投影的正交模格的情况下。这里的结果可能会为这一行的工作增添一些额外的视角。
英文摘要：
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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