#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 jhpalmieri):
It is ridiculous if the cohomology of a Lie group is not a graded Hopf
algebra. You can call it a Hopf superalgebra, but that is going against 50
years of usage, and using an unsigned version as the definition of a
graded Hopf algebra will confuse many mathematicians.
When I did an internet search on "graded Hopf algebra", most of the
results included the sign. (See
[http://preprints.ihes.fr/2006/M/M-06-40.pdf here] and
[http://www.math.lsa.umich.edu/~mityab/bloch-hopf/ here], and of course
there is Milnor and Moore's Annals paper.) Based on that and my own
experience, I really think that we cannot use `GradedHopfAlgebra` to mean
an unsigned version. It's obviously fine to implement the mathematical
concept, but don't call it a graded Hopf algebra.
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Ticket URL: <http://trac.sagemath.org/ticket/18675#comment:14>
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