#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 darij):
John: It is far from clear that Cartier uses your convention. He does
state some properties of super-Hopf algebras, without ever giving them a
name. Then, in §3, he defines a Hopf algebra in a way that does not
involve any super-structure. Maybe it is implicit in the twist map, but I
don't see much of a reason to assume it. In §4.1, Cartier gives an example
of "a graded Hopf algebra which is both commutative and cocommutative",
which only works if he does not use the Koszul sign rule. (Or does he ever
mention that he doubles degrees? As far as I understand, he does not, and
`Ch_1` is understood as the degree-1 component.)
I am not sure whether topologists are assuming the Koszul sign rule all
the time or only when they like it. But Hopf algebras haven't just been
the topologists' game for at least 20 years now. If you asked me for an
authoritative source on Hopf algebras, I'd probably come up with Sweedler,
Radford, Abe (in some order). Neither of them seems to impose the Koszul
sign rule on graded Hopf algebras.
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Ticket URL: <http://trac.sagemath.org/ticket/18675#comment:16>
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