Embeddings into Orthomodular Lattices with Given Centers,State Spaces and Automorphism Groups |
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| Authors: | Harding John Navara Mirko |
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| Institution: | (1) Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, U.S.A.;(2) Center for Machine Perception, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Praha, Czech Republic |
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| Abstract: | 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. |
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| Keywords: | automorphism group center measure orthomodular lattice orthomodular poset state |
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