Derivations on group algebras with coding theory applications

Leo Creedon, Kieran Hughes

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If RG is a group ring, where R is commutative and S is a set of generators of G then necessary and sufficient conditions on a map from S to RG are established, such that the map can be extended to an R-derivation of RG. Derivations are shown to be trivial for semisimple group algebras of abelian groups. The derivations of finite group algebras are constructed and listed in the commutative case and in the case of dihedral groups. In the dihedral case, the inner derivations are also classified. Lastly, these results are applied to construct well known binary codes as images of derivations of group algebras.

Original languageEnglish
Pages (from-to)247-265
Number of pages19
JournalFinite Fields and their Applications
Volume56
DOIs
Publication statusPublished - Mar 2019

Keywords

  • Coding theory
  • Derivations
  • Dihedral
  • Group algebra
  • Group ring

Name of Affiliated ATU Research Unit

  • MISHE - Mathematical Modelling and Intelligent Systems for Health & Environment

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