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nLab > Latest Changes: Hall algebra

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2011
    • (edited May 14th 2013)

    made Ben Webster’s recent observation the Idea-section at Hall algebra (see the link given there)

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeApr 19th 2011

    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.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2011

    In the entry he says he hasn’t seen this before and would be grateful for references. Maybe you could drop him (and the nnLab entry) some pointers to specific places where this perspective is discussed.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeApr 20th 2011
    • (edited Apr 20th 2011)

    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.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2013
    • (edited May 14th 2013)

    added a quick paragraph on the interpretation of Hall algebras via 2-Segal spaces by Dyckerhoff-Kapranov.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 6th 2014
    • (edited Jul 6th 2014)

    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.

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 6th 2014

    At motivic Hall algebra (I think the clipboard had the wrong link on it!)

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 6th 2014

    ah, thanks, fixed now.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 30th 2018

    Added in a reference

    but the bibliography could do with some annotation.

    diff, v14, current

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeOct 14th 2022
    • (edited Jun 20th 2023)

    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).

    diff, v17, current

    • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeJun 20th 2023
    • Mauro Porta, Francesco Salla, Two-dimensional categorified Hall algebras, J. Eur. Math. Soc. 25:3 (2023) 1113-1205 doi

    diff, v18, current

    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeJun 20th 2023

    Publication data for

    • Olivier Schiffmann, Eric Vasserot, The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials, Compositio Mathematica 147:1 (2011) 188-234 doi arXiv:0802.4001, (2008); The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of A 2\mathbf{A}^2, Duke Math. J. 162(2): 279-366 (2013) doi arXiv:0905.2555

    diff, v19, current

    • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeJun 20th 2023
    • (edited Jun 20th 2023)

    Publication data for

    diff, v19, current

    • CommentRowNumber14.
    • CommentAuthorzskoda
    • CommentTimeJun 20th 2023
    • (edited Jun 20th 2023)

    Publication data for

    diff, v19, current

    • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeSep 22nd 2023

    More references and some remarks on them.

    diff, v24, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeOct 29th 2023
    • (edited Oct 29th 2023)

    added pointer to

    While at it, I tried to polish up the list of references a bit.

    diff, v27, current

    • CommentRowNumber17.
    • CommentAuthorzskoda
    • CommentTimeNov 14th 2023

    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).

    diff, v28, current

1 to 17 of 17

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