Abstract
In this paper we study the problem of representing groups as groups of automorphisms on an orthomodular lattice or poset. This problem not only has intrinsic mathematical interest but, as we shall see, also has applications to other fields of mathematics and also physics. For example, in the “quantum logic” approach to an axiomatic quantum mechanics, important parts of the theory can not be developed any further until a fairly complete study of the representations of physical symmetry groups on orthomodular lattices is accomplished [1].We will consider two main topics in this paper. The first is the analogue of Schur's lemma and its corollaries in this general setting and the second is a study of induced representations and systems of imprimitivity.
Publisher
Canadian Mathematical Society
Cited by
10 articles.
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1. Test Spaces;Handbook of Quantum Logic and Quantum Structures;2009
2. Monoidal Categories, Symmetries, and Compound Physical Systems;International Journal of Theoretical Physics;2007-09-26
3. Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics;Current Research in Operational Quantum Logic;2000
4. Test Spaces and Orthoalgebras;Current Research in Operational Quantum Logic;2000
5. BACK MATTER;Measures and Hilbert Lattices;1986-10