Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics

Artur E. Ruuge () and Fred Van Oystaeyen ()
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Artur E. Ruuge: Vrije Universiteit Brussel (VUB) Pleinlaan 2, Faculteit Ingenieurswetenschappen
Fred Van Oystaeyen: Universiteit Antwerpen (UA), Middelheimlaan 1, Dept. Wiskunde-Informatica

Chapter 4 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 39-45 from Springer

Abstract: An orthoalgebra is a partial abelian monoid whose structure captures some properties of the direct sum operation of the subspaces of a Hilbert space. Given a physical system (quantum or classical), the collection of all its binary observables (properties) may be viewed as an orthoalgebra. In the quantum case, in contrast to the classical, the orthoalgebra cannot have a “bivaluation” (a morphism ending in a two-element orthoalgebra). An interesting combinatorial problem is to construct finite orthoalgebras not admitting bivaluations. In this paper we discuss the construction of a family such examples closely related to the irreducible root systems of exceptional type.

Keywords: Root System; Lift Property; Symplectic Vector Space; Empty Subset; Orthogonal Element (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-3-540-85332-9_4

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