Analysis of Indecomposable Representations of the Dihedral Group Dn over Fields of Characteristic 2

ZANGOOIEZADEH, EBRAHIM

doi:10.22075/ijnaa.2025.38428.5507

Analysis of Indecomposable Representations of the Dihedral Group Dn over Fields of Characteristic 2

Articles in Press

Document Type : Research Paper

Author

EBRAHIM ZANGOOIEZADEH

Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.

10.22075/ijnaa.2025.38428.5507

Abstract

This paper is dedicated to a thorough investigation of the representation theory of the dihedral group Dn over fields of characteristic 2. Unlike the classical theory over fields of characteristic zero, the structure and classification of indecomposable representations in characteristic 2 present unique challenges due to the subtleties introduced by modular representation theory and the presence of non-semi simplicity. We review foundational definitions, detail the decomposition of representations into indecomposables, and highlight key structural differences from the characteristic zero case. The classification results for finite dihedral groups over fields with characteristic 2 are emphasized, culminating in a comprehensive understanding of the representation types and their matrix realizations.

Keywords

Dihedral Group

Indecomposable Representations

Characteristic 2

Modular Representation Theor

Non-Semisimple Structures