Elements of Lie Groups and Algebras

This lecture covers the transformation of vectors and tensors in quantum physics, focusing on Lie groups and algebras. It explains the concept of reducible representations, possible states of rotational systems, and the distance between elements in a group. The instructor discusses the transformation according to different representations, the generators of Lie groups, and the unitary property of transformations. The lecture also delves into the structure constants of groups, the concept of simple connectedness, and the covering groups. It concludes with a detailed explanation of the smallest connected group and the modifications of forms in different groups.