Lie group decomposition refers to the process of breaking down a Lie group into simpler components, typically into a product of subgroups, which can provide insights into the structure and representation of the group. This concept is particularly important in areas such as differential geometry, representation theory, and theoretical physics. There are several common forms of decomposition related to Lie groups: 1. **Direct Product Decomposition**: A Lie group can often be expressed as a product of simpler Lie groups.
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