Induction and restriction on representations of dihedral groups

TL;DR

This paper investigates the algebraic structures formed by induction and restriction operations on modules over dihedral groups, providing detailed descriptions under specific order conditions.

Contribution

It characterizes the relations, basis, center, and indecomposable decomposition of these algebras for dihedral groups with orders not divisible by four.

Findings

Describes relations and basis of the algebras

Identifies the center of the algebras

Provides decomposition into indecomposable modules

Abstract

We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the center, and a decomposition into indecomposables of these algebras.