Talk:Universal enveloping algebra

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Mathematics rating:	Start Class	High Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Arcfrk 06:56, 21 May 2007 (UTC)

I changed the first sentence of "direct construction." It used to say "For general reasons having to do with universal properties..." the thing is unique if it exists. I thought this wording was oblique at best and incorrect at worst. Most directly, one would probably prove uniqueness from the universal property via some standard abstract nonsense argument. There's probably some way to formulate things so that the proof is seen as following from a "general reason," but more likely I would say it follows from a "standard method." Either way, the present wording, hinting, imprecisely and mysteriously , at grandiose ideas doesn't seem helpful. Either stick with my approach (though please reword it-- I don't know if my wording is ideal) or describe the proof-process in a little more detail, if you're going to mention it. Lewallen 01:55, 12 March 2007 (UTC)

the first sentence of the section which i renamed "Alternate Construction", namely "Noting that any associative K-algebra becomes a Lie algebra with the bracket [a,b] = a.b-b.a, a construction and precise..." i added this sentence to some stuff i put at the top in some explanatory stuff. if this stuff stays at the top, then this sentence should be removed from the "alternate Construction" section, because it would be redundant. i didn't remove it myself, because i couldn't figure out how to start the paragraph without it. need help of the author (i assume this is you, Charles?) - Lethe

I've been through this again, mainly format matters, but some moves of material.

Charles Matthews 14:45, 13 May 2004 (UTC)

Charles, do we have the ability to make commutative diagrams?

There are some examples (Clifford algebra, IIRC correctly). Mostly from the old days, and not very nice. Or, people make little graphics to upload.

My taste is to use words, anyway. This really isn't a mathematics text, from the point of view of exposition.

Charles Matthews 21:24, 13 May 2004 (UTC)

OK then. another question: i put the universal construction on top of the less abstract construction, but looking around a bit (e.g. Tensor product) it seems that the preference is to start with the less abstract, and save the universal property for later. what do you think?

Not a big deal, either way. In this case, relying on tensor algebra, it's kind of clear what to do. Charles Matthews 11:37, 14 May 2004 (UTC)