A4,2

The Lie-algebra A_ (4, 2) is defined via the adjoint map (1,2)-tensor ad

A02 = ad = Table2ad[2 Τ[({{0, 0, 0, a e_1}, {0, 0, 0, e_2}, {0, 0, 0, e_2 + e_3}, {0, 0, 0, 0}})]] ; [adJacobi[ad]] ;

where a≠0.

The automorphism group of the Lie-algebra is generated by the following matrices:

M = Algebra[4, Τdα[ad, 1, #1] &, ] ;

ShowMat[EXP[λ #1] &/@M]

Investigation: b_1≠0,b_5≠0

Investigation: b_1≠0,b_5=0

Investigation: b_1=0

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