Elizabeth Bolduc Terika Harris Lie Algebras

Lie Algebras: Definition

A Misconception Marius Sophus Lie Norwegian Mathematician Geometry and differential equations

Lie Groups Differentiable manifold Such that the operations are compatible with the smooth structure. Examples

How do Lie Algebras Relate to Lie Groups? Lie Algebras help us understand Lie Groups. If G is a Lie Group, the Lie Algebra of G is defined as the tangent space of the identity element of G.

Hermann Weyl Introduced in 1930 Character Formula Symmetry

Lie Algebras: Definition

Example

Example: Cross Product

Example Abelian Lie Algebra If every bracket product is zero Question: can you name this Abelian Lie Algebra?

Lie Algebras: Definition

Conclusion Every Lie Group has a corresponding Lie Algebra. Lie Algebras help us understand Lie Groups