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I am trying to understand the derivation of the Lorentz generators but I am stuck.

I am reading this paper at the moment: http://arxiv.org/pdf/1103.0156.pdf

I don't understand the following step in equation 15 on page 3:

[itex]\omega^{\alpha}_{\beta}=g^{\alpha\mu}\omega_{\mu\beta}[/itex]

I don't understand how this can be true. I mean g is not the identity matrix.

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# Lorentz Group Generators

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