Graded Hopf algebras#
- sage.categories.graded_hopf_algebras.GradedHopfAlgebras(base_ring)[source]#
The category of graded Hopf algebras.
EXAMPLES:
sage: C = GradedHopfAlgebras(QQ); C Join of Category of Hopf algebras over Rational Field and Category of graded algebras over Rational Field and Category of graded coalgebras over Rational Field sage: C is HopfAlgebras(QQ).Graded() True
>>> from sage.all import * >>> C = GradedHopfAlgebras(QQ); C Join of Category of Hopf algebras over Rational Field and Category of graded algebras over Rational Field and Category of graded coalgebras over Rational Field >>> C is HopfAlgebras(QQ).Graded() True
Note
This is not a graded Hopf algebra as is typically defined in algebraic topology as the product in the tensor square \((x \otimes y) (a \otimes b) = (xa) \otimes (yb)\) does not carry an additional sign. For this, instead use
super Hopf algebras
.