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.

]]>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…)

]]>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

Yes, sorry, antisubalgebra.

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

]]>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 $f$?

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