Super Hopf algebras with basis¶
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class
sage.categories.super_hopf_algebras_with_basis.
SuperHopfAlgebrasWithBasis
(base_category)¶ Bases:
sage.categories.super_modules.SuperModulesCategory
The category of super Hopf algebras with a distinguished basis.
EXAMPLES:
sage: C = HopfAlgebras(ZZ).WithBasis().Super(); C Category of super hopf algebras with basis over Integer Ring sage: sorted(C.super_categories(), key=str) [Category of super algebras with basis over Integer Ring, Category of super coalgebras with basis over Integer Ring, Category of super hopf algebras over Integer Ring]
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class
ParentMethods
¶ Bases:
object
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antipode
()¶ The antipode of this Hopf algebra.
If
antipode_basis()
is available, this constructs the antipode morphism fromself
toself
by extending it by linearity. Otherwise,self.antipode_by_coercion()
is used, if available.EXAMPLES:
sage: A = SteenrodAlgebra(7) sage: a = A.an_element() sage: a, A.antipode(a) (6 Q_1 Q_3 P(2,1), Q_1 Q_3 P(2,1))
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class