index_38.html

A4,8

$ShowSol[A08, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→ -2 b_5^(1/2) b_8^(1/2)}]$

$We consider the Lie-algebra with commutator<br /> ad = ( {{0, 0, 0, 0}, {0, 0, e_1, e_2}, {0, -e_1, 0, -e_3}, {0, -e_2, e_3, 0}} )$

$and the scalar product of the form ℬ = ( {{0, 0, 0, -2 b_5^(1/2) b_8^(1/2)}, {0, b_5, b_6, b_7}, {0, b_6, b_8, b_9}, {-2 b_5^(1/2) b_8^(1/2), b_7, b_9, b_10}} )$

$ShowSol[A08, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→2 b_5^(1/2) b_8^(1/2)}]$

$We consider the Lie-algebra with commutator<br /> ad = ( {{0, 0, 0, 0}, {0, 0, e_1, e_2}, {0, -e_1, 0, -e_3}, {0, -e_2, e_3, 0}} )$

$and the scalar product of the form ℬ = ( {{0, 0, 0, 2 b_5^(1/2) b_8^(1/2)}, {0, b_5, b_6, b_7}, {0, b_6, b_8, b_9}, {2 b_5^(1/2) b_8^(1/2), b_7, b_9, b_10}} )$

Created by Mathematica (September 15, 2007)