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nLab > Latest Changes: augmented A-infinity algebra

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 19th 2013
    • CommentRowNumber2.
    • CommentAuthorjim_stasheff
    • CommentTimeJun 20th 2013
    The title is a bit misleading since you have something much more spectral in mind. Some misprints in the references.
    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeJun 20th 2013
    (I'm just testing something ... Andrew)
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2013
    • (edited Jun 20th 2013)

    Thansk, Jim.

    I have now added a warning remark here about a possible simplicial meaning of augmentation that one might think of.

    Also I have fixed some misprints. (Possiby I did introduce new misprints though… ;-)

    • CommentRowNumber5.
    • CommentAuthorjim_stasheff
    • CommentTimeJun 21st 2013
    Not sure I made my point clear; there is the notion of augmentation for an Aoo-algebra pure and simple
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 21st 2013

    there is the notion of augmentation for an Aoo-algebra pure and simple

    Hm, you mean a notion different from the pure and simple “equipped with a map to the base ∞\infty-ring”, as in the entry?

    Maybe you just want me to make a distinction between on the one hand A ∞A_\infty-algebras in characteristic 0, hence in chain complexes and on the other the general notion of A ∞A_\infty-algebras in spectra? If so, I’d ask: why? The simple definition of augmentation does not depend on this.

    • CommentRowNumber7.
    • CommentAuthorJon Beardsley
    • CommentTimeJun 22nd 2013

    Haha, speaking of misprints: I know of a mathematician named Gregory Arone, but not Fregory Arone! :-)

    • CommentRowNumber8.
    • CommentAuthorjim_stasheff
    • CommentTimeJun 22nd 2013
    Urs,
    I just meant without invoking $E_\infty$
    • CommentRowNumber9.
    • CommentAuthorjim_stasheff
    • CommentTimeJun 22nd 2013
    Urs, I just meant without invoking Eoo
    • CommentRowNumber10.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 22nd 2013

    Jim, in case this helps, you can render LaTeX in comments by first clicking on Markdown+Itex, where it says “Format comments as” below the comment box.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2013

    Jim,

    I have added:

    to the base E-∞ ring (which might be a plain commutative ring).

    Does that help?

    • CommentRowNumber12.
    • CommentAuthorjim_stasheff
    • CommentTimeJun 23rd 2013
    yes, that helps
    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2014

    added to the Definition-section of augmented A-infinity algebra a pointer to the very general definition 5.2.3.14 in Higher Algebra.

1 to 13 of 13

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