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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 28th 2011

    I have been writing up for the Menagerie (later to be adapted for the Lab), a version of Turaev’s crossed GG-algebras. These are G-graded algebra for a group GG which are Frobenius and also have a ’crossed’ G-action on them. Two questions:

    (i) in the entry on graded algebra in the nLab there is a requirement that GG be Abelian, but Turaev’s notion does not require this. Is this important for the Lab entry?

    (ii) I think that a graded GG-algebra should lead to an automorphism crossed module / 2-group, basically U(L)Aut(L)U(L)\to Aut(L). Has anyone seen anything that mentions this (other than my paper with Turaev, where we use it). It should be a ’well-known’ construction, but I have not yet found it anywhere. It depends on giving a graded G-algebra as a single object (?) monoidal category endowed with a functor (having some properties) to the category BGBG.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2011

    Is this important for the Lab entry?

    I wouldn’t think it is generally. For some applications it will be. Both cases should be discussed.

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 28th 2011

    I have upgraded graded algebra :-)