Retrieving "Hodge Star Operator" from the archives

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1. Exterior Derivative

   Linked via "Hodge star operator"

   | Divergence | Vector field $\mathbf{V}$ (via its dual 2-form) | $k=2$ | $\text{d}\alpha$ | $\text{div} \mathbf{V}$ (with a sign convention) |
   Note that the standard identification of divergence in terms of the exterior derivative requires mapping the vector field $\mathbf{V}$ to its corresponding 2-form $\alpha$ via the Hodge star operator ($\star$), i.e., $\text{div} \mathbf{V} = (-1)^{n(n-1)/2} \star (\text{d} (\star \omega))$, where $\omega$ is the [1-form](/e…