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Next video: https://youtu.be/erA0jb9dSm0 Lie's theory of continuous symmetries was originally for differential equations, but turns ...

Notes are on my GitHub! github.com/rorg314/WHYBmaths In this video I introduce the one dimensional unitary group U(1).

Part 3: https://youtu.be/ZRca3Ggpy_g Around 11:50, can't imagine that this error got in - it should have been SU(n) = {U in U(n), ...

Keywords: Lie groups, Lie algebras, exponential map, adjoint action, commutators, representation theory, characters, highest ...

Lie Groups encode the symmetry of systems. We examine actions of a Lie group on a vector space, given their algebraic, ...

AZScreenRecorder This is my video recorded with AZ Screen Recorder. It's easy to record your screen and livestream. Download ...

Before you rush to the comments to yell at Stephanie about the thumbnail or the title of the video...know that this was all MY doing!

Support the channel Patreon: https://www.patreon.com/michaelpennmath Merch: ...

All right so I'm going to be talking about what are called Li Group integrators and the basic idea behind Lee Group integrators are ...

We discuss the abstract definition of a Lie algebra.

We prove that any torus is contained in a maximal torus, which completes our proof that nontrivial maximal tori exist in compact ...

We introduce the adjoint representation and find the weight diagrams for the adjoint representations of sl(2,C) and sl(3,C).

We work out in detail how the off-diagonal elements of the Lie algebra act in the Sym^2(C^2) representation of SU(2), confirming ...

We discuss the representation theory of SU(2) and lay out the plan for the next few videos. We finish by discussing morphisms of ...

We introduce the Killing form on a Lie algebra, and calculate it for some matrices in sl(3,C).

... processing as i groups are sometime useful yes and deformation deformation of images are related to discrete group action and ...

Garrett Lisi at FQXi's 5th International Conference.

Notes are on my GitHub! github.com/rorg314/WHYBmaths This video will expand on the previous video discussing SO(2) (2D ...

Hello guys, this is a continuation of our lecture series in Group Theory, particularly, Lie Groups. I hope you enjoy and if you have ...

We define tori and maximal tori. These will be the replacement for general compact groups of the subgroups of diagonal matrices ...