29
Lindell
Theresa
en
13
Norm Inequalities in Zeon Algebras
2019-04-11T12:40
false
https://link.springer.com/10.1007%2Fs00006-018-0934-z
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.
https://scigraph.springernature.com/explorer/license/
articles
2019-02-01
2019-02
research_article
10.1007/s00006-018-0934-z
doi
Mathematical Sciences
dimensions_id
pub.1110713049
Staples
G. Stacey
Pure Mathematics
Springer Nature - SN SciGraph project
Advances in Applied Clifford Algebras
0188-7009
1661-4909
99e60d3ae293959e3385d18c9abd8024e58d19d11cf03c6d22b6ee92a7d9e05d
readcube_id
1
Southern Illinois University Edwardsville
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, 62026-1653, Edwardsville, IL, USA