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made Ben Webster’s recent observation the Idea-section at Hall algebra (see the link given there)
I suppose, this is not only his recent observation I suppose, at least Kontsevich/Soibelman often do this theory in terms of constructible sheaves and did not consider that aspect new when they jumped into the area.
In the entry he says he hasn’t seen this before and would be grateful for references. Maybe you could drop him (and the $n$Lab entry) some pointers to specific places where this perspective is discussed.
OK, I will try, once I am back to normal work schedule. By the way I am not saying that it is precisely this statement (there are many variants of Hall algebra construction) but that some of them are superimposable to the Grothendieck group of constructible sheaves on SOME associated moduli space, there are variants.
added a quick paragraph on the interpretation of Hall algebras via 2-Segal spaces by Dyckerhoff-Kapranov.
added a brief paragraph on motivic Hall algebras (really just a glorified pointer to the literature).
In the course of this I thought we’d need a dedicated entry Calabi-Yau 3-fold (in a sequence with elliptic curves and K3s), so I created one.
At motivic Hall algebra (I think the clipboard had the wrong link on it!)
ah, thanks, fixed now.
Added in a reference
but the bibliography could do with some annotation.
Article
has discovered the 2-Segal spaces and the general construction of Hall algebras independently. Decomposition spaces are unital 2-Segal spaces (in a bit different defining exposition).
Publication data for
Publication data for
Publication data for
added pointer to
While at it, I tried to polish up the list of references a bit.
I just wrote review for
You can read the preview at the link. I put several weeks of work in making sure I understand the paper enough to write it and I think that the review is useful (though short of so many beautiful aspects of this excellent paper).
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