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I have a problem with one thing.

Let's consider the Lorentz group and the vicinity of the unit matrix. For each $\hat{L}$ from such vicinity one can prove that there exists only one matrix $\hat{\epsilon}$ such that $\hat{L}=exp[\hat{\epsilon}]$. If we take $\epsilon^{\mu \nu},\ \mu < \nu$, as the parameters on the Lorentz group in a vicinity of the unit matrix, then we can compute the corresponding Killing vectors as $\xi_{\alpha \beta}^{\mu}=\frac{\partial x^{'\mu}}{\partial \epsilon^{\alpha \beta}}\left(\hat{\epsilon}=0 \right) $ where $x^{'\mu}=L^{\mu}_{\nu}x^{\nu}$. Here is my problem: during the computations there is one line that I do not get, namely: $\cfrac{\partial L^{\mu \nu}}{\partial \epsilon^{\alpha \beta}}\left(\hat{\epsilon}=0 \right)=\delta^{\mu}_{\alpha}\delta^{\nu}_{\beta}-\delta^{\mu}_{\beta}\delta^{\nu}_{\alpha} $. The $(\epsilon^{\mu \nu})$ matrix is antisymmetric, so that is why we get the difference of the Kronecer delta?

Thank you in advance!

MW

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