Primitive central idempotents of a finite group over a field

Satyam Shukla; Jagmohan Tanti

Primitive central idempotents of a finite group over a field

Representation Theory 2026-08-04 v1 Rings and Algebras

Authors: Satyam Shukla , Jagmohan Tanti

Abstract

We give a method to compute the primitive central idempotents of a semi-simple finite group algebra associated with an irreducible character $\chi$ such that for every $g\in G$ , either $\chi(g) = 0$ or all eigenvalues of $\rho(g)$ have the same order. We then show several consequences which highlight the significance and possible applications of our approach.

Keywords

primitive central idempotents semi-simple group algebra irreducible character eigenvalues finite group

Cite

@article{arxiv.2608.03371,
  title  = {Primitive central idempotents of a finite group over a field},
  author = {Satyam Shukla and Jagmohan Tanti},
  journal= {arXiv preprint arXiv:2608.03371},
  year   = {2026}
}