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Irreducible representations of generalised Kac-Paljutkin Hopf algebras

Sebastian Halbig, Christian Lomp

Abstract

The aim of this note is to provide a self-contained classification of the irreducible representations of generalised Kac--Paljutkin Hopf algebras, recently introduced by the second author.

Irreducible representations of generalised Kac-Paljutkin Hopf algebras

Abstract

The aim of this note is to provide a self-contained classification of the irreducible representations of generalised Kac--Paljutkin Hopf algebras, recently introduced by the second author.

Paper Structure

This paper contains 6 sections, 12 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Generalised Kac--Paljutkin algebras and wreath products
  3. Representations of wreath products
  4. Clifford theory
  5. Irreducible representations of symmetric groups
  6. Proof of the main theorem

Key Result

Theorem 1

Let $\Bbbk$ be an algebraically closed field of characteristic zero and fix two positive integers $2 \leq n,m \in \mathbb{N}$. The generalised Kac--Paljutkin $\Bbbk$-Hopf algebra $H_{n,m}$ is isomorphic as an algebra to the group algebra $\Bbbk[ \mathbb{Z}_{n} \wr S_{m}]$. Its irreducible representa

Theorems & Definitions (36)

  • Theorem 1: Theorem \ref{['thm:the-one-we-want']}
  • Definition 2.1
  • Remark 2.2
  • Lemma 2.3
  • Definition 2.4
  • Lemma 2.5
  • proof
  • Definition 2.6
  • Definition 2.7
  • Remark 2.8
  • ...and 26 more