2013/04/16 by David J. Foulis, Foulis, David J., Sylvia Pulmannova +1
Mathematics · Physics and Astronomy · #06F25 #81P10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:06F25 #msc:81P10
paper · pdf · doi:10.48550/arxiv.1304.4378
arxiv created 2013/04/16 · arxiv updated 2013/04/17
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence relation on the projection lattice of the algebra induced by finite sequences of symmetries. In case the projection lattice is complete, or even centrally orthocomplete, this equivalence relation is shown to possess many of the properties of a dimension equivalence relation on an orthomodular lattice.