#18675: Add 'connected' as a class for graded Hopf algebras with basis.
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Reporter: kdilks | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.8
Component: algebra | Resolution:
Keywords: days65 | Merged in:
Authors: Jean-Baptiste | Reviewers: zabrocki
Priez | Work issues:
Report Upstream: N/A | Commit:
Branch: | 174d2288c77874c17750339dfef5400a8dccce8c
public/ticket/18675 | Stopgaps:
Dependencies: |
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Changes (by jhpalmieri):
* status: needs_review => needs_work
Comment:
What does `GradedConnectedHopfAlgebraOfInteger` mean? It seems like a
terrible name to me. I would suggest changing it, or if not, explaining
the terminology. From the name, it sounds like there is one Hopf algebra
element (`t^n`) for each integer `n`. If this element is placed in degree
`n`, then since `n` can be any integer (given name of the algebra), it is
not connected.
I have another issue with this: the coproduct does not define a graded
Hopf algebra. In a graded Hopf algebra, the Koszul sign convention comes
into play, so the coproduct on `t^2` is `(1 tensor t + t tensor 1)^2 = 1
tensor (t^2) + (t^2) tensor 1`: the two `t tensor t` terms cancel. You
should grade it instead by putting `t` in degree 2.
A typo: in the method `one_basis`: {{{EXAMPLES::r}}}. Delete the "r".
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Ticket URL: <http://trac.sagemath.org/ticket/18675#comment:6>
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