Exponential Maps: Properties and Applications in Lie Groups

Related lectures (32)

Page 2 of 4

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explains vector fields as derivations and their algebraic structure in Lie algebra.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Explores the properties of the exponential map in Lie groups and algebras.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.

Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.