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Semisimplicial Unital Groups

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Abstract

If there is an order-preserving group isomorphism from a directed abelian group G with a finitely generated positive cone G + onto a simplicial group, then G is called a semisimplicial group. By factoring out the torsion subgroup of a unital group having a finite unit interval, one obtains a semisimplicial unital group. We exhibit a representation for the base-normed space associated with a semisimplicial unital group G as the Banach dual space of a finite dimensional order-unit space that contains G as an additive subgroup. In terms of this representation, we formulate necessary and sufficient conditions for G to be archimedean.

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Authors and Affiliations

  1. Emeritus Professor of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003;, 1 Sutton Court, Amherst, MA 01002, USA

    David J. Foulis

  2. Department of Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA 71272, USA

    Richard J. Greechie

Authors
  1. David J. Foulis
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  2. Richard J. Greechie
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Foulis, D.J., Greechie, R.J. Semisimplicial Unital Groups. International Journal of Theoretical Physics 43, 1689–1704 (2004). https://doi.org/10.1023/B:IJTP.0000048814.76568.de

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  • DOI: https://doi.org/10.1023/B:IJTP.0000048814.76568.de

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