1Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA
2Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73, Bratislava, Slovakia
Tóm tắt
AbstractA synaptic algebra is a generalization of the Jordan algebra of self-adjoint 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.
