  In a previous paper, we investigated the Hopf algebra structure in string
theory and gave a unified formulation of the quantization of the string and the
space-time symmetry. In this paper, this formulation is applied to the case
with a nonzero B-field background, and the twist of the Poincare symmetry is
studied. The Drinfeld twist accompanied by the B-field background gives an
alternative quantization scheme, which requires a new normal ordering. In order
to obtain a physical interpretation of this twisted Hopf algebra structure, we
propose a method to decompose the twist into two successive twists and we give
two different possibilities of decomposition. The first is a natural
decomposition from the viewpoint of the twist quantization, leading to a new
type of twisted Poincare symmetry. The second decomposition reveals the
relation of our formulation to the twisted Poincare symmetry on the Moyal type
noncommutative space.
