Properties of the Exponential Map

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 1 of 4

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Integral Curves and Exponential Map

Explores integral curves on manifolds and the significance of the exponential map in Lie groups.

Lie Algebra: Vector Space and Multiplication Law

Covers Lie Algebra, focusing on vector space and multiplication law.

Subgroups and subalgebras

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.

Nilpotent Lie Groups

Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.

Complete Reducibility of Complex Representations

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.