The Brauer group BM(k,D_n, R_z) of the dihedral group

Let p^m be a power of a prime number p, D_{p^m} be the dihedral group of order 2p^m and k be a field where p is invertible and containing a primitive 2p^m-th root of unity. The aim of this paper is computing the Brauer group BM(k, R,) of the group Hopf algebra of D_{p^m} with respect to the quasi-triangular structure R_z arising from the group Hopf algebra of the cyclic group Z_{p^m} of order p^m, for z coprime with p. The main result states that BM(k, D_{p^m}, R_z) is isomorphic to Z(2) x k/k(2) x Br(k) when p is odd and when p = 2, BM (k, D_{2^m}, R_z) is isomorphic to Z(2) X Z(2) x k/k(2) x k/k(2) x Br(k).