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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 28th 2011
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI have been writing up for the Menagerie (later to be adapted for the Lab), a version of Turaev's crossed $G$-algebras. These are G-graded algebra for a group $G$ 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 $G$ be Abelian, but Turaev's notion does not require this. Is this important for the Lab entry? (ii) I think that a graded $G$-algebra should lead to an automorphism crossed module / 2-group, basically $U(L)\to Aut(L)$. 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 $BG$.

   I have been writing up for the Menagerie (later to be adapted for the Lab), a version of Turaev’s crossed $G$-algebras. These are G-graded algebra for a group $G$ 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 $G$ be Abelian, but Turaev’s notion does not require this. Is this important for the Lab entry?

   (ii) I think that a graded $G$-algebra should lead to an automorphism crossed module / 2-group, basically $U(L)\to Aut(L)$. 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 $BG$.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 28th 2011
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI have upgraded [[graded algebra]] :-)

   I have upgraded graded algebra :-)