Discovering Sparse Representations of Lie Groups with Machine Learning
This provides a general method for finding infinitesimal generators for any Lie group, which is incremental as it builds on existing deep learning approaches for symmetry transformations.
The paper tackled the problem of deriving sparse representations of arbitrary Lie algebras by extending deep learning techniques for symmetry transformations, successfully reproducing canonical sparse representations for the Lorentz group and U(n)/SU(n) families.
Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.