F4 (Mathematics)

Algebra

Dynkin diagram

Roots of F₄

$(\backslash pm\; 1,\backslash pm\; 1,0,0)$

$(\backslash pm\; 1,0,\backslash pm\; 1,0)$

$(\backslash pm\; 1,0,0,\backslash pm\; 1)$

$(0,\backslash pm\; 1,\backslash pm\; 1,0)$

$(0,\backslash pm\; 1,0,\backslash pm\; 1)$

$(0,0,\backslash pm\; 1,\backslash pm\; 1)$

$(\backslash pm\; 1,0,0,0)$

$(0,\backslash pm\; 1,0,0)$

$(0,0,\backslash pm\; 1,0)$

$(0,0,0,\backslash pm\; 1)$

$(\backslash pm\backslash frac\{1\}\{2\},\backslash pm\backslash frac\{1\}\{2\},\backslash pm\backslash frac\{1\}\{2\},\backslash pm\backslash frac\{1\}\{2\})$

$(0,0,0,1)$

$(0,0,1,-1)$

$(0,1,-1,0)$

$(\backslash frac\{1\}\{2\},-\backslash frac\{1\}\{2\},-\backslash frac\{1\}\{2\},-\backslash frac\{1\}\{2\})$

Weyl/Coxeter group

Cartan matrix

F₄ lattice

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