As per the title: where did the notation $a\wedge b$ for the exterior product of $a$ and $b$ originate, and/or who popularised it? I'm especially interested in motivation for the choice of this symbol (which also means "and" in logic and "meet" in order theory).
I've moved this question here from MSE, where it got very little attention despite offering a bounty; the original version is pasted below the line because it includes a bit about my reason for asking.
It seems odd that something that looks so much like a join [see below] would get given "the wrong symbol". It's even worse when you dualise it and get something called (quite reasonably) the "meet product", but write that as $A\vee B$.
I'm aware the answer might be "it just turned out that way", but was this choice of symbol motivated by a natural way to think of $A\wedge B$ as a meet in some lattice or other?
If not, which historical figure should I blame for this situation? I understand Grassmann wrote $A\wedge B$ as $[A, B]$, which would let him off the hook.
Intuitively, if I have two vectors $a$ and $b$, $a\wedge b$ is the smallest object that contains both $a$ and $b$. If you order elements of the exterior algebra by inclusion, which seems very natural if you're doing geometry, you get a lattice where the join operation is the exterior product.
This mostly seems to come to the fore in Clifford-algebra-related approaches to geometry. Examples of people mentioning this relationship and complaining about / altering the standard notation:
While digging up these references I also turned up a claim that Peano wrote the exterior product using $\vee$, whereas Cartan used $\wedge$, but it's not clear to me whether Cartan originated (or popularised) this notation or whether he had a particular reason for choosing it [or indeed whether this claim is correct -- it was an offhand remark with no citation].