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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2024
    • (edited Oct 1st 2024)

    Currently “anti-ideal” redirects to antisubalgebra, which is less than helpful.

    I’d like to give it it’s own entry.

    But what’s a good canonical reference? Especially on anti-ideals in Lie algebras?

    I am asking because I ran into the following (simple) situation, which I’d like to address by its proper name:

    Given an L L_\infty-algebra 𝔤\mathfrak{g} such that its CE-algebra CE(𝔤)CE(\mathfrak{g}) has generators (e i) iI(e^i)_{i \in I} and one more generator ff which is closed, df=0\mathrm{d} f = 0, then discarding that generator yields the CE-algebra of a sub-L L_\infty-algebra.

    This sub-algebra, I suppose, wants to be called the “quotient by the abelian anti-ideal” which is generated by the element dual to ff?

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeOct 1st 2024
    • (edited Oct 1st 2024)

    nnLab currently does not have a page named antialgebra (nor anti-algebra). Did you mean antisubalgebra ?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2024

    Yes, sorry, antisubalgebra.

  1. I don’t know about anti-ideals in Lie algebras but for anti-ideals in commutative rings there is

    • A. S. Troelstra and D. van Dalen. Constructivism in mathematics. Vol. II, volume 123 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam, 1988
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2024

    Thanks. I’ll make a little entry now

    (Let’s see if the software will post the announcement to this thread here or start a new one…)

  2. The software will post the announcement on a new thread because this thread is located in the “Atrium > Mathematics, Physics & Philosophy” subforum while the announcements are posted in the “nLab > Latest Changes” subforum.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2024