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]

class