2018/08/16 by Kieran Hughes, Hughes, Kieran, Leo Creedon +1 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1808.05381
openalex publication_date 2018/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.