Graded Lie Conformal Algebras¶

AUTHORS:

Reimundo Heluani (2019-10-05): Initial implementation.

class sage.categories.graded_lie_conformal_algebras.GradedLieConformalAlgebras(base_category)[source]¶

Bases: GradedLieConformalAlgebrasCategory

The category of graded Lie conformal algebras.

EXAMPLES:

Sage

sage: C = LieConformalAlgebras(QQbar).Graded(); C                               # needs sage.rings.number_field
Category of H-graded Lie conformal algebras over Algebraic Field

sage: CS = LieConformalAlgebras(QQ).Graded().Super(); CS
Category of H-graded super Lie conformal algebras over Rational Field
sage: CS is LieConformalAlgebras(QQ).Super().Graded()
True

Python

>>> from sage.all import *
>>> C = LieConformalAlgebras(QQbar).Graded(); C                               # needs sage.rings.number_field
Category of H-graded Lie conformal algebras over Algebraic Field

>>> CS = LieConformalAlgebras(QQ).Graded().Super(); CS
Category of H-graded super Lie conformal algebras over Rational Field
>>> CS is LieConformalAlgebras(QQ).Super().Graded()
True

class sage.categories.graded_lie_conformal_algebras.GradedLieConformalAlgebrasCategory(base_category)[source]¶

Bases: GradedModulesCategory

Super(base_ring=None)[source]¶

Return the super-analogue category of self.

INPUT:

base_ring – this is ignored

EXAMPLES:

Sage

sage: # needs sage.rings.number_field
sage: C = LieConformalAlgebras(QQbar)
sage: C.Graded().Super() is C.Super().Graded()
True
sage: Cp = C.WithBasis()
sage: Cp.Graded().Super() is Cp.Super().Graded()
True

Python

>>> from sage.all import *
>>> # needs sage.rings.number_field
>>> C = LieConformalAlgebras(QQbar)
>>> C.Graded().Super() is C.Super().Graded()
True
>>> Cp = C.WithBasis()
>>> Cp.Graded().Super() is Cp.Super().Graded()
True