A4,12

ShowSol[A12, ( {{0, 0, b_3, b_4}, {0, b_5, b_6, b_7}, {b_3, b_6, b_8, b_9}, {b_4, b_7, b_9, b_10}} ), {b_3→b_7, b_4→ -b_6, b_5→0}]

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

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

with determinant |ℬ| = b_6^4 + 2 b_6^2 b_7^2 + b_7^4 .

The Ricci curvature tensor is zero…4×4

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