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SFP, Lie Algebra (4) (Killing Form (13) (Inner Product on Dual Space (15)…

- - - - Simple Roots
        and Properties (18)
        
        Cartan Matrix
        and Properties (19)
        
        Dynkin Diagrams (20)
        
        Cartan Classification (20)
        
        Root System from
        Cartan Matrix (20)
        
        Root Lattice (21)
  - - - Root Strings (16)
        
        Real Inner Product
        of Roots (17)
        
        Roots Span
        Dual Space (17)
      - Chevalley Basis /
        Serre Relation (19)
        
        Weight Lattice /
        Fundamental Weights (21)
      - Weight Set (20)
- - - - L(SO(3)) =
        L(SU(2)) (6)
      - Exponential Map (7)
        
        Baker-Campbell-
        Hausdorff Formula (8)
        
        SO(3) =
        SU(2) / Z2 (8)
        
        SU(2) Group
        Elements (11)
      - Lie Algebra Repn.
        from Lie Group Repn. (9)
  - - - L(SU(2)) Basis /
        Step Operators (10)
    - - Highest Weight (22)
    - - L(SU(2)) Weights (10)
        
        Littlewood-Richardson
        Coefficients (12)
        
        Tensor Product
        Weight Set (22)
        
        Standard Model (25)

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SFP

Weight Lattice /
Fundamental Weights (21)

Manifold (1)

Symmetry (1)

Lie Group (1)

Gauge Symmetry (2)

Smooth
Manifold (2)

GL(n),
SL(n) (2)

O(n), SO(n) (3)

Compact
Set (3)

Simply-Connected
Space (3)

SO(3) Manifold
Topology (3)

Group (1)

U(n), SU(n) (4)

Lie Algebra (4)

Structure
Constants (4)

Ideals and
Simple LAs (5)

Tangent
Space (5)

Lie Algebra from
Lie Group (6)

Homomorphism/
Isomorphism (4)

L(SO(3)) =
L(SU(2)) (6)

Diffeomorphism (7)

Vector Field (7)

Exponential Map (7)

Representation (8)

Baker-Campbell-
Hausdorff Formula (8)

SO(3) =
SU(2) / Z2 (8)

Lie Algebra Repn.
from Lie Group Repn. (9)

Ad-map /
Adjoint Repn. (9)

Irreducible Repn. (10)

L(SU(2)) Basis /
Step Operators (10)

Weights (10)

L(SU(2)) Weights (10)

SU(2) Group
Elements (11)

Direct Sum of
Repns. (11)

Tensor Product
Repn. (11)

Littlewood-Richardson
Coefficients (12)

Killing Form (13)

Cartan's Theorem /
Semi-Simple LAs (13)

Cartan Subalgebra (14)

Roots /
Dual Space (14)

Cartan-Weyl Basis (15)

Inner Product on
Dual Space (15)

Root Strings (16)

Compact Type /
Complexification (17)

Real Inner Product
of Roots (17)

Roots Span
Dual Space (17)

Root Lengths
and Angles (18)

Simple Roots
and Properties (18)

Cartan Matrix
and Properties (19)

Chevalley Basis /
Serre Relation (19)

Dynkin Diagrams (20)

Cartan Classification (20)

Root System from
Cartan Matrix (20)

Weight Set (20)

Weight Lattice /
Fundamental Weights (21)

Root Lattice (21)

Highest Weight (22)

Tensor Product
Weight Set (22)

Unitary Repn.
in QM (23)

Infinitessimal Symm.
Transformations (23)

Covariant Derivative (24)

Maxwell Theory (24)

Non-Abelian
Gauge Theory (25)

Gauge-Field Lagrangian (25)

Standard Model (25)