Super algebras with basis

class sage.categories.super_algebras_with_basis.SuperAlgebrasWithBasis(base_category)

Bases: sage.categories.super_modules.SuperModulesCategory

The category of super algebras with a distinguished basis

EXAMPLES:

sage: C = Algebras(ZZ).WithBasis().Super(); C
Category of super algebras with basis over Integer Ring
class ParentMethods
graded_algebra()

Return the associated graded module to self.

See AssociatedGradedAlgebra for the definition and the properties of this.

See also

graded_algebra()

EXAMPLES:

sage: W.<x,y> = algebras.DifferentialWeyl(QQ)
sage: W.graded_algebra()
Graded Algebra of Differential Weyl algebra of
 polynomials in x, y over Rational Field
class SignedTensorProducts(category, *args)

Bases: sage.categories.signed_tensor.SignedTensorProductsCategory

The category of super algebras with basis constructed by tensor product of super algebras with basis.

extra_super_categories()

EXAMPLES:

sage: Algebras(QQ).Super().SignedTensorProducts().extra_super_categories()
[Category of super algebras over Rational Field]
sage: Algebras(QQ).Super().SignedTensorProducts().super_categories()
[Category of signed tensor products of graded algebras over Rational Field,
 Category of super algebras over Rational Field]

Meaning: a signed tensor product of super algebras is a super algebra

extra_super_categories()

EXAMPLES:

sage: C = Algebras(ZZ).WithBasis().Super()
sage: sorted(C.super_categories(), key=str) # indirect doctest
[Category of graded algebras with basis over Integer Ring,
 Category of super algebras over Integer Ring,
 Category of super modules with basis over Integer Ring]