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The efficient fusion of global and local multi-scale features is quite important for remote sensing scene classification (RSSC). The scenes in high-resolution remote sensing images (HRRSI) contain many complex backgrounds, intra-class diversity, and inter-class similarities. Many studies have shown that global features and local features are helpful for RSSC. The receptive field of a traditional convolution kernel is small and fixed, and it is difficult to capture global features in the scene. The self-attention mechanism proposed in transformer effectively alleviates the above shortcomings. However, such models lack local inductive bias, and the calculation is complicated due to the large number of parameters. To address these problems, in this study, we propose a classification model of global-local features and attention based on Lie Group space. The model is mainly composed of three independent branches, which can effectively extract multi-scale features of the scene and fuse the above features through a fusion module. Channel attention and spatial attention are designed in the fusion module, which can effectively enhance the crucial features in the crucial regions, to improve the accuracy of scene classification. The advantage of our model is that it extracts richer features, and the global-local features of the scene can be effectively extracted at different scales. Our proposed model has been verified on publicly available and challenging datasets, taking the AID as an example, the classification accuracy reached 97.31%, and the number of parameters is 12.216 M. Compared with other state-of-the-art models, it has certain advantages in terms of classification accuracy and number of parameters. [ABSTRACT FROM AUTHOR]