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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 $f$?
$n$Lab currently does not have a page named antialgebra (nor anti-algebra). Did you mean antisubalgebra ?
Yes, sorry, antisubalgebra.
I don’t know about anti-ideals in Lie algebras but for anti-ideals in commutative rings there is
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…)
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.
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