Lie Algebra and Lie Groups: Structure and Applications

This presentation offers an introduction to Lie algebras and Lie groups, exploring their definitions, properties, and interconnections. It delves into the smoothness and operations defining Lie groups, as well as the types and classifications of Lie algebras. Applications in geometry, physics, and representation theory are highlighted, alongside advanced topics like structure constants and their implications for mathematical physics. Designed to provide a foundational and applied...