index_34.html

A4,2

$ShowSol[A02/.{a-> -b_3^2/(b_3^2 - 2 b_1 b_8)}, ( {{b_1, b_2, b_3, 0}, {b_2, 0, b_6, b_7}, {b_3, b_6, b_8, b_9}, {0, b_7, b_9, b_10}} ), {b_2->0, b_6->0}]$

$and the scalar product of the form ℬ = ( {{b_1, 0, b_3, 0}, {0, 0, 0, b_7}, {b_3, 0, b_8, b_9}, {0, b_7, b_9, b_10}} )$

$ShowSol[A02/.{a→1}, ( {{b_1, b_2, b_3, 0}, {b_2, 0, b_6, b_7}, {b_3, b_6, b_8, b_9}, {0, b_7, b_9, b_10}} ), {b_2→0, b_6→0}]$

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

$and the scalar product of the form ℬ = ( {{b_1, 0, b_3, 0}, {0, 0, 0, b_7}, {b_3, 0, b_8, b_9}, {0, b_7, b_9, b_10}} )$

$ShowSol[A02/.{a-> (-b_5^2 + 4 b_6^2 - 4 b_5 b_8)/(4 (b_6^2 - b_5 b_8))}, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2->0, b_3->0}]$

$and the scalar product of the form ℬ = ( {{0, 0, 0, b_4}, {0, b_5, b_6, b_7}, {0, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} )$

$ShowSol[A02/.{a→ -1}, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2→0, b_5→0, b_6→0}]$

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

$and the scalar product of the form ℬ = ( {{0, 0, b_3, b_4}, {0, 0, 0, b_7}, {b_3, 0, b_8, b_9}, {b_4, b_7, b_9, b_10}} )$

$ShowSol[A02/.{a→1}, ( {{0, b_2, b_3, b_4}, {b_2, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_2->0, b_5->0}]$

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

$and the scalar product of the form ℬ = ( {{0, 0, b_3, b_4}, {0, 0, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} )$

Created by Mathematica (September 15, 2007)