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 [math]k \subseteq h[/math].

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