index_39.html

A4,10

$ShowSol[A10, ( {{0, b_2, b_3, b_4}, {b_2, b_5, 0, b_7}, {b_3, 0, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→ -b_8/3, b_5→ (4 b_8)/3}]$

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

$and the scalar product of the form ℬ = ( {{0, 0, 0, -b_8/3}, {0, (4 b_8)/3, 0, b_7}, {0, 0, b_8, b_9}, {-b_8/3, b_7, b_9, b_10}} )$

$ShowSol[A10, ( {{0, b_2, b_3, b_4}, {b_2, b_5, 0, b_7}, {b_3, 0, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→b_8/3, b_5→ (4 b_8)/3}]$

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

$and the scalar product of the form ℬ = ( {{0, 0, 0, b_8/3}, {0, (4 b_8)/3, 0, b_7}, {0, 0, b_8, b_9}, {b_8/3, b_7, b_9, b_10}} )$

$ShowSol[A10, ( {{0, b_2, b_3, b_4}, {b_2, b_5, 0, b_7}, {b_3, 0, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→b_5 - b_8}]$

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

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

$ShowSol[A10, ( {{0, b_2, b_3, b_4}, {b_2, b_5, 0, b_7}, {b_3, 0, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_3→0, b_4→b_8 - b_5}]$

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

$and the scalar product of the form ℬ = ( {{0, 0, 0, -b_5 + b_8}, {0, b_5, 0, b_7}, {0, 0, b_8, b_9}, {-b_5 + b_8, b_7, b_9, b_10}} )$

Created by Mathematica (September 15, 2007)