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nLab > Latest Changes: Gerstenhaber algebra

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2010

    created stub for Gerstenhaber algebra

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 25th 2010
    • (edited Nov 25th 2010)

    “is essentially a Poisson algebra internal to a category of chain complexes”

    I think there is some more precise statement which I often forget, like its shift by plus or minus 1 is internal analog of a Poisson algebra. If somebody can nail this down.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2010

    I added Cohen’s theorem that the Gerstenhaber-algebra operad is the homolpogy of the little disks operad in chain complexes. (need to track down precise reference).

    I need to make clearer in various enttries now the distinction between little disks and framed little disks…

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2024
    • (edited Jun 25th 2024)

    I tried to add some clarification to the Idea-section:

    1. that Gerstenhaber algebras are graded Poisson algebras with bracket of degree -1 (for which I added pointer to Cattaneo, Fiorenza & Longoni 2006, Def. 1.1)

    2. that some authors more generally call a graded Poisson algebra with bracket of any odd degree a “Gerstenhaber algebra”,

    where “some authors” is at least Kontsevich 1999, Thm. 3.

    (This in reply to somebody asking me how to read Konsevich at that point. If anyone more familiar with the graded algebra community than me can expand on the terminology conventions, please do.)

    diff, v10, current

1 to 4 of 4

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