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I'm trying to find the generators of the Lorentz group. Jackson lists them all, for example, the generator of a boost along x is:

[tex]

K=\left( \begin{array}{c}

0\;1\;0\;0 \\

1\;0\;0\;0 \\

0\;0\;0\;0 \\

0\;0\;0\;0

\end{array} \right)

[/tex]

Now, what I don't understand is: this matrix is a covariant, contravariant, or mixed tensor? I mean, should I write

[tex]K_{\mu\nu}\:\:,\:\:K_{\mu}\;^{\nu}\:\:,\:\:K^{\mu \nu}...[/tex] or what else?

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# Homework Help: Lorentz generators

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