Norm Inequalities in Zeon Algebras View Full Text


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Article Info

DATE

2019-02

AUTHORS

Theresa Lindell, G. Stacey Staples

ABSTRACT

The zeon (“nil-Clifford”) algebra Cℓnnil can be thought of as a commutative analogue of the n-particle fermion algebra and can be constructed as a subalgebra of a Clifford algebra. Combinatorial properties of the algebra make it useful for applications in graph theory and theoretical computer science. In this paper, the zeon p-norms and infinity norms are introduced. The 1-norm is shown to be the only sub-multiplicative p-norm on zeon algebras. Multiplicative inequalities involving the infinity norm (which is not sub-multiplicative) are developed and equivalence of norms in Cℓnnil is used to establish a number of multiplicative inequalities between p-norms and the infinity norm. As an application of norm inequalities, necessary and sufficient conditions for convergence of the zeon geometric series are established, and the series limit is expressed as a finite sum. The exposition is supplemented by a number of examples computed using Mathematica. More... »

PAGES

13

References to SciGraph publications

  • 2017-06. Zeon Roots in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • 2018-03. Elementary Functions and Factorizations of Zeons in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • 2008-09. A New Adjacency Matrix for Finite Graphs in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • 2017-12. Hamiltonian Cycle Enumeration via Fermion-Zeon Convolution in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 2008-02. Norms and Generating Functions in Clifford Algebras in ADVANCES IN APPLIED CLIFFORD ALGEBRAS
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    http://scigraph.springernature.com/pub.10.1007/s00006-018-0934-z

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    http://dx.doi.org/10.1007/s00006-018-0934-z

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