#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):
When you compute `(1 tensor t + t tensor 1)^2`, there is a term `(1 tensor
t) (t tensor 1)`. When these are multiplied, you have to apply the twist
map (interchanging the middle two terms). That has a sign involved:
`(-1)^{(deg t) (deg t)} = -1`. So you get a summand `- t tensor t` in the
coproduct. This cancels with the term `(t tensor 1) (1 tensor t)`.
That is, in the main diagram defining a bialgebra,
[https://en.wikipedia.org/wiki/Bialgebra like the first one here, for
example], the twist map `\tau` has a sign in the graded case.
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Ticket URL: <http://trac.sagemath.org/ticket/18675#comment:8>
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