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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 64, Issue 3


Symmetries in synaptic algebras

David Foulis / Sylvia Pulmannová
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0238-2


A 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.

MSC: Primary 81P10, 47L30; Secondary 46L70, 06C15

Keywords: synaptic algebra; Jordan algebra; order-unit space; projection; symmetry equivalence of projections; relative center property

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 751–776, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0238-2.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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