Choreography refers to creation of dance steps and motions for dances according to the latent knowledge in human mind, where the created dance motions are in general style-specific and consistent. So far, such latent style-specific knowledge about dance styles cannot be represented explicitly in human language and has not yet been learned in previous works on music-to-dance generation tasks. In this paper, we propose a novel music-to-dance synthesis framework with controllable style embeddings. These embeddings are learned representations of style-consistent kinematic abstraction of reference dance clips, which act as controllable factors to impose style constraints on dance generation in a latent manner. Thus, the dance styles can be transferred to dance motions by merely modifying the style embeddings. To support this study, we build a large music-to-dance dataset. The qualitative and quantitative evaluations demonstrate the advantage of our proposed framework, as well as the ability of synthesizing diverse styles of dances from identical music via style embeddings.