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$\begingroup$ Form the points in this answer, it also follows quite easily that the cross product itself is more closely related to planes and areas, and is thus more naturally understood in terms of two-forms. $\endgroup$
– Toffomat
Commented Dec 16, 2021 at 6:30
$\begingroup$ I like the idea of poly-indexing the kernel to represent a poly-vector. Your example is $\mathbf{\hat e}_{ij}=\mathbf{\hat e}_i\wedge\mathbf{\hat e}_j.$ $\endgroup$
– Steven Thomas Hatton
Commented Dec 16, 2021 at 21:25
$\begingroup$ Oh, I see. There is a difference between the currently marketed German language version and the translation I'm using. link.springer.com/book/10.1007/978-3-642-97861-6 $\endgroup$
– Steven Thomas Hatton
Commented Dec 17, 2021 at 0:07

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