#18044: Implement categories for super algebras/modules
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: categories | Resolution:
Keywords: super | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/super_categories-18044|
0ce1cad1332ec34909c4baa2761307a3bd205ef8
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by darij):
Sorry but the assumption that "super X are graded X" (or just "super X are
X") is fundamentally wrong. The longer we keep it in, the harder it will
be to cross that bridge. It already causes wrong results:
{{{
sage: C = HopfAlgebras(QQ).Super()
sage: C.super_categories()
[Category of hopf algebras over Rational Field,
Category of super algebras over Rational Field]
}}}
Super Hopf algebras are not Hopf algebras. In a Hopf algebra,
` (xy)_{(1)} \otimes (xy)_{(2)} = x_{(1)} y_{(1)} \otimes x_{(2)} y_{(2)}
`
(using sumfree Sweedler notation), while in a super Hopf algebra,
` (xy)_{(1)} \otimes (xy)_{(2)} = (-1)^{\deg y_{(1)} \deg x_{(2)}} x_{(1)}
y_{(1)} \otimes x_{(2)} y_{(2)} `.
In other news: In the `lift_module_morphism` method for Clifford algebras,
did you really mean `Graded` in
{{{
return Cl.module_morphism(on_basis=f, codomain=self,
category=AlgebrasWithBasis(self.base_ring()).Graded())
}}}
(and not `Super`)?
--
Ticket URL: <http://trac.sagemath.org/ticket/18044#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
