Idempotent elements of the group algebra

Authors

  • Vicent Miralles Lluch Universitat Politècnica de València

Keywords:

idempotent elements, splitting fields, group algebra, Galois action, finite fields

Abstract

The purpose of this work is to study the centrally primitive idempotent elements of the group algebra and develop a method for calculating them in the case of finite fields. Based on the theory of representations of finite groups and results on modules, algebras and field extensions, the concept of a splitting field for a group is introduced. Finally, it explores how the Galois action on the group algebra defined over these fields allows these idempotents of the original field to be obtained.

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Published

2025-12-04

How to Cite

Miralles Lluch, V. (2025). Idempotent elements of the group algebra. Reports@SCM, 10(1), 87–88. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/155903

Issue

Vol. 10 No. 1 (2025)

Section

Extended abstracts

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