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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 2nd 2011
    • CommentRowNumber2.
    • CommentAuthorjim_stasheff
    • CommentTimeApr 2nd 2011
    I find it very misleading to put Linfty in the title
    since it is just a plain old dg Lie
    and indeed the commutator dg Lie of the assoc End.

    What is the meaning or significance of referring to an inner Lie alg?
    Some of the indices are messed up.
    Note that the internal differential is itself in End
    and hence acts as an inner

    Regarding it as Linfty will be relevant only when mapping to or from it
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2011

    Jim, please help me, how can it be “very misleading” if it is “relevant for mapping to or from it”?

    If an object that looks like X needs to be regarded as Y for understanding its morphisms, then I think it makes thinks clearer to think of it as a Y.

    But I don’t want to fight about such terminology issues. I have changed the title of the entry. The text already commented on this issue before.

    • CommentRowNumber4.
    • CommentAuthorjim_stasheff
    • CommentTimeApr 5th 2011
    Misleading only in that one might then be looking to see where some non-trivial higher brackets are lurking
    An asscoative algebra is a special case of an Aoo-alg but I wouldn't want to define it that way
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2011

    I did define end(V)end(V) as a dg-Lie algebra. But I called the entry “endomorphism \infty-Lie algebra” because I think what is most important about this dg-Lie algebra is to know that it is a model for the endomorphism Lie algebra in an \infty-context.

    Around here we routinely say “Lie 2-algebra” for something coming from a differential crossed module. But a differential crossed module is just a certain dg-Lie algebra. Nevertheless, calling it not a crossed module and not a dg-Lie algebra but a Lie 2-algebra is good: it reminds us that the concrete implementation of this gadget as this or that is not so important, but that what is important is its meaning as a higher Lie algebra.

    In this spirit I thought (and still think, to be frank) that there ought to be an entry called “endomorphism \infty-Lie algebra” which discusses the abstract concept and its models by dg-Lie algebras or by other things.

    But anyway, let’s not fight over terminology anymore. Let’s save our energy for more substantial discussions!

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