Super Hopf algebras with basis¶
- class sage.categories.super_hopf_algebras_with_basis.SuperHopfAlgebrasWithBasis(base_category)¶
Bases:
sage.categories.super_modules.SuperModulesCategoryThe 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]
- class ParentMethods¶
Bases:
object- antipode()¶
The antipode of this Hopf algebra.
If
antipode_basis()is available, this constructs the antipode morphism fromselftoselfby 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))