I have been doing a self-study of Differential Forms and Exterior Calculus using the book "Applied Exterior Calculus" by Dominic Edelen (Dover Publication).
I ran across an operator that apparently represents the inner product of a differential form on a vector. Quoted below is equation 3-4.3 of the Edelen book:
The operator symbol that I have not seen before is the backward L symbol between the $V$ and $\omega$ to the left of the first equal sign. Clearly it is defining an inner product as noted by other expressions shown.
As I have never seen this before and have not found any other reference to this symbol I am curious as to its origin or even if it has a name.
Therefore, who invented this, what is it called, and is it now obsolete or just so rarely used as I have not found it in other sources. I have a number of other texts on differential forms as it is not used in any of them as far as I have found.
This is the interior product, often written $\iota_V\omega$. This is an example of a contraction. It is defined more generally for any $k$-form $\omega$, resulting in a $(k-1)$-form: $$\iota_V\omega (v_1,\dots,v_{k-1}) = \omega(V,v_1,\dots,v_{k-1}).$$