Graded Lie Conformal Algebras - Category Framework

Skip to content
Back to top
View this page
Edit this page

# Graded Lie Conformal Algebras

AUTHORS:

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

class sage.categories.graded_lie_conformal_algebras.GradedLieConformalAlgebras(base_category)

  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)

  Bases: `GradedModulesCategory`

  Super(base_ring=None)

    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