#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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Comment (by zabrocki):
> 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.
I agree that the name could be clearer, but I don't understand the
relation to the Koszul sign convention. This example is testing the
functionality of graded connected Hopf algebra and demonstrates how an
example of this category should be implemented (a free combinatorial Hopf
algebra with one primitive generator in degree one). What you are
describing is a quotient of the Hopf algebra that is implemented here.
I have a few more edits that I will push shortly.
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Ticket URL: <http://trac.sagemath.org/ticket/18675#comment:7>
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