Finitely Generated Lie Conformal Algebras

AUTHORS:

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

class sage.categories.finitely_generated_lie_conformal_algebras.FinitelyGeneratedLieConformalAlgebras(base_category)

Bases: CategoryWithAxiom_over_base_ring

The category of finitely generated Lie conformal algebras.

EXAMPLES:

sage: LieConformalAlgebras(QQbar).FinitelyGenerated()                           # needs sage.rings.number_field
Category of finitely generated Lie conformal algebras over Algebraic Field

class Graded(base_category)

Bases: GradedModulesCategory

The category of H-graded finitely generated Lie conformal algebras.

EXAMPLES:

sage: LieConformalAlgebras(QQbar).FinitelyGenerated().Graded()              # needs sage.rings.number_field
Category of H-graded finitely generated Lie conformal algebras
 over Algebraic Field

class ParentMethods

Bases: object

some_elements()

Some elements of this Lie conformal algebra.

Returns a list with elements containing at least the generators.

EXAMPLES:

sage: V = lie_conformal_algebras.Affine(QQ, 'A1',                       # needs sage.combinat sage.modules
....:                                   names=('e', 'h', 'f'))
sage: V.some_elements()                                                 # needs sage.combinat sage.modules
[e, h, f, K, ...]
sage: all(v.parent() is V for v in V.some_elements())                   # needs sage.combinat sage.modules
True

class Super(base_category)

Bases: SuperModulesCategory

The category of super finitely generated Lie conformal algebras.

EXAMPLES:

sage: LieConformalAlgebras(AA).FinitelyGenerated().Super()                  # needs sage.rings.number_field
Category of super finitely generated Lie conformal algebras
 over Algebraic Real Field

class Graded(base_category)

Bases: GradedModulesCategory

The category of H-graded super finitely generated Lie conformal algebras.

EXAMPLES:

sage: LieConformalAlgebras(QQbar).FinitelyGenerated().Super().Graded()  # needs sage.rings.number_field
Category of H-graded super finitely generated Lie conformal algebras
 over Algebraic Field