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# Exterior covariant derivative and Lie derivative in Penrose abstract index notation?

2017-12-03 03:06:28

How does one express the Lie derivative of tensors, and exterior covariant derivative for forms with values in a vector bundle in Penrose abstract index notation? I've tried looking through Penrose's negative dimensional tensors article but didn't see it written down.

For say a vector-bundle valued 3-form $\omega_{bcd}^A$ where upper case indices correspond to the vector bundle and lower case indices are form indices, would the exterior covariant derivative just be $\nabla_{[a}\omega_{bcd]}^A$, where square brackets indicate antisymmetrization?