In this study, we present a generic solution of emotional data exchange between heterogeneous multi-modal applications. This proposal is based on a new algebraic representation of emotions and is composed of three distinct layers : the psychological layer, the formal computational layer and the language layer. The First layer represents the psychological theory adopted in our approach. The second layer is a formal multidimensional model that matches the psychological approach of the first layer. In the language layer, we propose to extend the current implementation of EmotionML [1] to generate the final emotional data to be transferred through the network. We propose to modify the EmotionML vocabulary in order to represent emotions in our vector model defined in the formal computational layer.