Almost Split Sequences of the Quantum Double of a Finite Group

Let $k$ be a field of characteristic $p>0$, and $G$ be a finite group of order divisible by $p$. We prove that the almost split sequences of the quantum double $D(kG)$ can be constructed from those of group algebras, where the groups run over all centralizer subgroups of representatives of conjugate classes of $G$. As a special case, we give an application to the quantum double of dihedral groups.