The Representations of Quantum Double of Dihedral Groups

Abstract

Let $k$ be an algebraically closed field of odd characteristic $p$, and let $D_n$ be the dihedral group of order $2n$ such that $p\mid 2n$. Let $D(k{D}_n)$ denote the quantum double of the group algebra $k{D}_n$. In this paper, we describe the structures of all finite dimensional indecomposable left $D(k{D}_n)$-modules, equivalently, of all finite dimensional indecomposable Yetter-Drinfeld $k{D}_n$-modules, and classify them.

15 pages, to appear in Algebra Colloquium