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nLab > Latest Changes: universal enveloping algebra

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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeOct 5th 2011
    • (edited Oct 5th 2011)

    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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 12th 2012

    Minor additions and reorganization at universal enveloping algebra.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2023
    • (edited Nov 25th 2023)

    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 AA for Lie(A)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:

    diff, v19, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2023

    While I was at it, I have now also reworded the lines under “Isomorphism problem” (here), which previously had been somewhat odd (also dating from rev 1).

    diff, v19, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2023
    • (edited Nov 26th 2023)

    added pointer to:

    and more details to:

    diff, v20, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2023

    added a section “Relation to the group algebra” (here), so far (lazily) only with a direct quote of a paragraph from Hochschild 1981.

    diff, v20, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2023

    also pointer to Thm. 1 in:

    diff, v20, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2023

    added (here) mentioning of the example of Weyl algebras

    (following the analogous edit here)

    diff, v23, current

1 to 8 of 8

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