Simple Grammar Problem: Is "a" or "the" Ideal in Lie Algebra?

[topsquark]

My slight confusion here is probably a simple grammatical problem.

Let h and k be ideals of a Lie algebra g.

Now let h be a maximal solvable ideal (i.e.one enclosed in no larger solvable ideal) of g. If k is any other solvable ideal, then so is h + k, and thus the maximality requirement implies h + k = h and hence \(\displaystyle k \subseteq h\).

My question is about the "a." I'm thinking that it should be "the." Aren't all ideals subalgebras of the maximal ideal?

Also: How do you pronounce "Lie?" Is it "lee" or "lye?"

-Dan

 

[MarkFL]

...Also: How do you pronounce "Lie?" Is it "lee" or "lye?"

-Dan

It is "lee":

https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Lie_algebra.html

 

[Fallen Angel]

Hi,

There is only one maximal solvable ideal, but the "a" fits better than a "the", because the uniqueness is proved after you have choose the maximal solvable ideal. (Sometimes I'm too demanding, huh?(Wondering)).

This ideal is also called the radical of the Lie algebra g (It will probably appear just after this proof if you have read it on a book.)

 

[topsquark]

Hi,

There is only one maximal solvable ideal, but the "a" fits better than a "the", because the uniqueness is proved after you have choose the maximal solvable ideal. (Sometimes I'm too demanding, huh?(Wondering)).

This ideal is also called the radical of the Lie algebra g (It will probably appear just after this proof if you have read it on a book.)

It's a good point. And yes, the text did immediately then show uniqueness. I didn't consider the logical order there since I already knew the maximal solvable ideal was unique.

Thanks!

-Dan

 

[blue_raver22]

Hello Dan,

Thank you for sharing your question. You are correct that the grammatical error in this context is a minor one, but it is important to clarify for the sake of clear communication. In this case, it would be more accurate to use "the" instead of "a" before "maximal solvable ideal" because the sentence is referring to a specific ideal, not just any ideal.

Regarding the pronunciation of "Lie," it is commonly pronounced as "lee" in English. However, in its native German, it would be pronounced as "lee-uh." Both pronunciations are acceptable in the mathematical context.

I hope this helps clarify the issue for you. Keep up the good work in your studies!

Best,