2023/12/19 by Manju, Praveen, Sharma, Rajendra Kumar
#16S34 #16W25 #20C05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2312.12215
In this article, we study the derivations of group algebras of some important groups, namely, dihedral (D2n), Dicyclic (T4n) and Semi-dihedral (SD8n). First, we explicitly classify all inner derivations of a group algebra \mathbbFG of a finite group G over an arbitrary field \mathbbF. Then we classify all \mathbbF-derivations of the group algebras \mathbbFD2n, \mathbbFT4n and \mathbbF(SD8n) when \mathbbF is a field of characteristic 0 or an odd rational prime p by giving the dimension and an explicit basis of these derivation algebras. We explicitly describe all inner derivations of these group algebras over an arbitrary field. Finally, we classify all derivations of the above group algebras when \mathbbF is an algebraic extension of a prime field.