Deep neural networks based purely on attention have been successful across several domains, relying on minimal architectural priors from the designer. In Human Action Recognition (HAR), attention mechanisms have been primarily adopted on top of standard convolutional or recurrent layers, improving the overall generalization capability. In this work, we introduce Action Transformer (AcT), a simple, fully selfattentional architecture that consistently outperforms more elaborated networks that mix convolutional, recurrent, and attentive layers. In order to limit computational and energy requests, building on previous human action recognition research, the proposed approach exploits 2D pose representations over small temporal windows, providing a low latency solution for accurate and effective real-time performance. Moreover, we open-source MPOSE2021, a new large-scale dataset, as an attempt to build a formal training and evaluation benchmark for real-time short-time human action recognition. Extensive experimentation on MPOSE2021 with our proposed methodology and several previous architectural solutions proves the effectiveness of the AcT model and poses the base for future work on HAR.