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An old query removed from universal enveloping algebra and archived here:
Eric: Is this a special case of universal enveloping algebra as it pertains to Lie algebras? I thought the concept of a universal enveloping algebra was more general than this. I scribbled some notes here. They are far from rigorous, but the references at the bottom of the page are certainly rigorous. I don’t remember them being confined to Lie algebras. I’m likely confused.
[Edit: Oh! I see now. From enveloping algebra you link to this page and call it enveloping algebra of a Lie algebra. Would that be a better name for this page? Or maybe universal enveloping algebra of a Lie algebra? Something to make it clear this page is specific to Lie algebras?]
Zoran: if you read the above article than you see that it distingusihes the enveloping algebra of a Lie algebra and universal enveloping algebra of a Lie algebra which is a universal one among all such. There is also an enveloping algebra of an associative algebra what is a different notion.
Also added to universal enveloping algebra, a link to a MathOverflow question What is the universal enveloping algebra which is looking for a rather general construction in a class of symmetric monoidal pseudoabelian categories. I also created a minimal literature section.
Minor additions and reorganization at universal enveloping algebra.
I have touched wording and formatting of the section “For Lie algebras” (here), for streamlining.
In particular, I deleted the words
In further we will just write $A$ for $Lie(A)$
(dating from rev 1) and adjusted the following notation accordingly.
Have also added a remark (here) on the generality of super Lie algebras such as of Whitehead brackets.
Finally, I added pointer to:
added pointer to:
and more details to:
also pointer to Thm. 1 in:
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