Year: 2024
Type: article
Abstract: Objectives: The purpose of this work is to study π-Bratteli diagrams arising from a class of group algebras πΎπΊπ and πΎππΊπ for every odd prime π, to define the irreducible representations using mutually orthogonal primitive idempotents and to index the complete set of irreducible representations for the group algebras πΎπΊπ and πΎππΊπ. Method: We use primitive idempotents to define irreducible representations and systematically index the irreducible representations to establish vertices for the π-Bratteli diagram. Also, we compute the matrix units using the orthogonal primitive idempotents of the group algebras πΎπΊπ and πΎππΊπ. Findings: The complete set of irreducible representations for the group algebras πΎπΊπ and πΎππΊπ has been successfully indexed, and matrix units for the group algebras πΎπΊπ and πΎππΊπ were determined using the orthogonal primitive idempotents. Novelty: This work provides a structured approach to constructing π-Bratteli diagrams for the group algebras related to odd primes, contributing new insights into their irreducible representations and matrix unitβs structures. Keywords: Primitive idempotent; Irreducible representation; Matrix units; Young diagram; Bratteli diagram
Authors: A Tamilselvi, D Hepsi
Institution: University of Madras
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407137203