Time dilation

Determinants and volume, revisited

Sign of a permutation

Lie groups and Lie algebras: Invariant theory (optional extra video)

Lie groups and Lie algebras: Decomposing into irreps

Lie groups and Lie algebras: Decomposing SU(3) representations

Lie groups and Lie algebras: Classification of SU(3) representations

Lie groups and Lie algebras: Further reading

Lie groups and Lie algebras: Classification of Dynkin diagrams

Lie groups and Lie algebras: Simple roots

Lie groups and Lie algebras: Classification of root systems, 2

Lie groups and Lie algebras: Dihedral angles

Lie groups and Lie algebras: Classification of root systems, 1

Lie groups and Lie algebras: Root systems

Lie groups and Lie algebras: Root spaces are 1-dimensional

Lie groups and Lie algebras: sl(2,C) subalgebras in general, 2

Lie groups and Lie algebras: sl(2,C) subalgebras in general, 1

Lie groups and Lie algebras: Dual Killing form and semisimplicity

Lie groups and Lie algebras: The Killing form

Lie groups and Lie algebras: The weight lattice

Lie groups and Lie algebras Optional Extra: Any torus is contained in a maximal torus

Lie groups and Lie algebras Optional Extra: Compact connected abelian groups are tori

Lie groups and Lie algebras Optional Extra: Finding compact abelian subgroups

Lie groups and Lie algebras: Maximal tori, overview

Lie groups and Lie algebras Optional Extra: Uniqueness of irreps with given highest weight

Lie groups and Lie algebras Optional Extra: Proof of classification of SU(3) irreps

Lie groups and Lie algebras: Duals

Lie groups and Lie algebras: The quark model

Lie groups and Lie algebras: Weyl symmetry

Lie groups and Lie algebras: Root vectors acting on weight spaces

Lie groups and Lie algebras: The adjoint representation

Lie groups and Lie algebras: SU(3) representations

Lie groups and Lie algebras: Classification of SU(2) representations

Lie groups and Lie algebras: X and Y example

Lie groups and Lie algebras: X and Y

Lie groups and Lie algebras: Weight space decomposition

Lie groups and Lie algebras: New representations from old

Lie groups and Lie algebras: Representations of SU(2), overview

Lie groups and Lie algebras: Representations of U(1), part 2

Lie groups and Lie algebras: Representations of U(1)

Lie groups and Lie algebras: Complete reducibility

Lie groups and Lie algebras: Representations

Lie groups and Lie algebras Optional Extra: Topology of Lie groups

Lie groups and Lie algebras: Example of a homomorphism SU(2) to SO(3)

Lie groups and Lie algebras: Lie's theorem on exponentiating homomorphisms

Lie groups and Lie algebras: Linearity

Lie groups and Lie algebras: One-parameter subgroups

Lie groups and Lie algebras: Smooth homomorphisms

Lie groups and Lie algebras Optional Extra: Convergence of exp

Lie groups and Lie algebras Optional Extra: Matrix norms

Lie groups and Lie algebras Optional Extra: Local exponential charts

Lie groups and Lie algebras: Little g is a Lie algebra

Lie groups and Lie algebras: Little g as a tangent space

Lie groups and Lie algebras: Lie algebras

Lie groups and Lie algebras: Example: SL(2,C)

Lie groups and Lie algebras: Example: O(n) (orthogonal matrices)

Lie groups and Lie algebras: The Lie algebra of a matrix Lie group

Lie groups and Lie algebras: The Baker-Campbell-Hausdorff formula

Lie groups and Lie algebras: A local logarithm

Lie groups and Lie algebras: Properties of the matrix exponential