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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2024
   • (edited Oct 1st 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexCurrently "[[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 $L_\infty$-algebra $\mathfrak{g}$ such that its CE-algebra $CE(\mathfrak{g})$ has generators $(e^i)_{i \in I}$ and one more generator $f$ which is closed, $\mathrm{d} f = 0$, then discarding that generator yields the CE-algebra of a sub-$L_\infty$-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 $f$?

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

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeOct 1st 2024
   • (edited Oct 1st 2024)
   • PermaLink
   Author: zskoda
   Format: MarkdownItex$n$Lab currently does not have a page named [[antialgebra]] (nor [[anti-algebra]]). Did you mean [[antisubalgebra]] ?

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, sorry, [[antisubalgebra]].

   Yes, sorry, antisubalgebra.

4. • CommentRowNumber4.
   • CommentAuthorMadeleine Birchfield
   • CommentTimeOct 1st 2024
   • PermaLink
   Author: Madeleine Birchfield
   Format: MarkdownItexI 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

   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
5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. 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...)

   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…)

6. • CommentRowNumber6.
   • CommentAuthorMadeleine Birchfield
   • CommentTimeOct 1st 2024
   • PermaLink
   Author: Madeleine Birchfield
   Format: MarkdownItexThe 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.

   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.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItex[right](https://nforum.ncatlab.org/discussion/18581/antiideal/?Focus=119353#Comment_119353)

   right