Embeddings into Orthomodular Lattices with Given Centers, State Spaces and Automorphism Groups

We prove that, given a nontrivial Boolean algebra B, a compact convex set S and a group G, there is an orthomodular lattice L with the center isomorphic to B, the automorphism group isomorphic to G, and the state space affinely homeomorphic to S. Moreover, given an orthomodular lattice J admitting at least one state, L can be chosen such that J is its subalgebra. Mathematics Subject Classifications (2000): 06C15, 81P10. Key words: automorphism group, center, measure, orthomodular lattice, orthomodular poset, state.

• Type: Journal
• Year: 2000
• Where: ORDER
• Authors: John Harding, Mirko Navara
• Keywords: Automorphism Group, Nontrivial Boolean Algebra, ORDER 2000, Orthomodular Lattice