I have five generators of a lie algebra, [tex]g_1,g_2,g_3,g_4,g_5[/tex] which at first glance I believe are independent, although I could be wrong.(adsbygoogle = window.adsbygoogle || []).push({});

I have calculated the structure constants, i.e.

[tex]\left[g_i,g_j\right]=f_{ij}^k g_k[/tex]

And from that I have calculated a matrix rep using [tex]\left(T_i\right)_j^k=f_{ij}^k[/tex]

I get [tex]T_1, T_2, T_3, T_4[/tex] all linearly independent.

However I get [tex]T_4=-T_5[/tex] which I do not understand. Does this mean there algebra is only 4D rather than 5D?

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# Lie algebra structure constants

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