Lie Algebra

Lie algebras, the tangent spaces of Lie groups, are fundamental mathematical structures increasingly crucial in various scientific fields. Current research focuses on leveraging Lie algebras in machine learning, particularly for designing equivariant neural networks and developing observers for systems evolving on Lie groups, often employing deep learning architectures to achieve this. This work addresses challenges like ensuring data privacy in quantum machine learning and improving the efficiency of control algorithms for mechanical systems, highlighting the importance of Lie algebraic methods for both theoretical advancements and practical applications in robotics and other areas. The development of efficient algorithms for computations on Lie groups and their algebras is a key driver of progress in these areas.