Title




Automorphisms of finite orthoalgebras, exceptional root systems and quantum mechanics
 
Author




 
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 twoelement 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. 
 
Language




English
 
Source (journal)




Generalized lie theory in mathematics, physics and beyond
 
Source (book)




International Workshop of BalticNordic Algebra, Geometry and, Mathematical Physics, OCT 1214, 2006, Lung Univ, Ctr Math Sci, Lund, SWEDEN
 
Publication




Berlin
:
Springer
,
2009
 
ISBN




9783540853312
 
Volume/pages




(2009)
, p. 3945
 
ISI




000264638600004
 
Full text (Publisher's DOI)




 
