Timeline for When a finite codimensional subalgebra contains a finite codimension ideal?
Current License: CC BY-SA 4.0
9 events
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| Apr 3, 2020 at 3:19 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
typos
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| Mar 20, 2020 at 20:15 | comment | added | Ali Taghavi | @SalvatoreSiciliano Thank you very much for your very interesting comment. I was not aware of the concept "restricted Lie algebra" | |
| Mar 20, 2020 at 18:55 | comment | added | Salvatore Siciliano | In my opinion, a possible classification of Lie algebras with the required property is hopeless. However, it is worth mentioning that examples of infinite-dimensional simple Lie algebras containing subalgebras of finite codimension were constructed by Amayo in a paper published in the Proc. Lond. Math. Soc. in 1976. On the other hand, by a Theorem of Kukin, if a restricted Lie algebra $L$ over a field of characteristic $p>0$ contains a restricted subalgebra of finite codimension, then $L$ also contains a restricted ideal of finite codimension, | |
| Mar 20, 2020 at 18:11 | comment | added | Ali Taghavi | @MarkSapir I think you are collecting some (and not all ) sufficient conditions which looks trivial. A classification is a "iff" theorem. For example I think it is the case for commutative unital $C^*$ algebra. Do you have a counter example? Moreover what about Lie algebra case? | |
| Mar 20, 2020 at 17:53 | comment | added | user6976 | What is a connection between the group theory problem and rings, $C*$-algebras and Lie algebras? An algebra has this property if it is finite or with 0-product (the product of any two elements is 0), or if every subalgebra of it is an ideal. A finite non-trivial field extension of an infinite field is a counterexample. There are lots of other similar trivial statements. I guess that is what you call "a classification". | |
| Mar 20, 2020 at 15:51 | comment | added | Ali Taghavi | @MarkSapir The motivation for this question is the pure group theoric problem written in the attached link you find in this pist "every finit index subgroup contains a finit index normal sibgroup". By classification I mean some results as "An algebra has this property if ......" or " An algebra has this property if and only if it satisfies......". Or some examples or counter examples. | |
| Mar 20, 2020 at 2:41 | comment | added | user6976 | What do you mean by classification? And why are you interested in this? | |
| Mar 19, 2020 at 22:09 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 199 characters in body
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| Mar 19, 2020 at 22:04 | history | asked | Ali Taghavi | CC BY-SA 4.0 |