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Affective computing is an important branch of artificial intelligence, and with the rapid development of brain computer interface technology, emotion recognition based on EEG signals has received broad attention. It is still a great challenge to effectively explore the multi-dimensional information in the EEG data in spite of a large number of deep learning methods. In this paper, we propose a deep model called Attention-based Multiple Dimensions EEG Transformer (AMDET), which can exploit the complementarity among the spectral-spatial-temporal features of EEG data by employing the multi-dimensional global attention mechanism. We transformed the original EEG data into 3D temporal-spectral-spatial representations and then the AMDET would use spectral-spatial transformer encoder layer to extract effective features in the EEG signal and concentrate on the critical time frame with a temporal attention layer. We conduct extensive experiments on the DEAP, SEED, and SEED-IV datasets to evaluate the performance of AMDET and the results outperform the state-of-the-art baseline on three datasets. Accuracy rates of 97.48%, 96.85%, 97.17%, 87.32% were achieved in the DEAP-Arousal, DEAP-Valence, SEED, and SEED-IV datasets, respectively. We also conduct extensive experiments to explore the possible brain regions that influence emotions and the coupling of EEG signals. AMDET can perform as well even with few channels which are identified by visualizing what learned model focus on. The accuracy could achieve over 90% even with only eight channels and it is of great use and benefit for practical applications.