On the center of the small quantum group

Using the quantum Fourier transform , we describe the block decomposition and multiplicative structure of a subalgebra of the center of the small quantum group at a root of unity. It contains the known subalgebra , which is isomorphic to the algebra of characters of finite-dimensional -modules. We prove that the intersection coincides with the annihilator of the radical of . Applying representation-theoretical methods, we show that surjects onto the algebra of endomorphisms of certain indecomposable projective modules over . In particular, this leads to the conclusion that the center of coincides with in the case .