Lie Conformal Algebras With Basis

AUTHORS:

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

class sage.categories.lie_conformal_algebras_with_basis.LieConformalAlgebrasWithBasis(base_category)

Bases: CategoryWithAxiom_over_base_ring

The category of Lie conformal algebras with basis.

EXAMPLES:

sage: LieConformalAlgebras(QQbar).WithBasis()                                   # needs sage.rings.number_field
Category of Lie conformal algebras with basis over Algebraic Field

class FinitelyGeneratedAsLambdaBracketAlgebra(base_category)

Bases: CategoryWithAxiom_over_base_ring

The category of finitely generated Lie conformal algebras with basis.

EXAMPLES:

sage: C = LieConformalAlgebras(QQbar)                                       # needs sage.rings.number_field
sage: CWF = C.WithBasis().FinitelyGenerated(); CWF                          # needs sage.rings.number_field
Category of finitely generated Lie conformal algebras with basis
 over Algebraic Field
sage: CWF is C.FinitelyGenerated().WithBasis()                              # needs sage.rings.number_field
True

class Graded(base_category)

Bases: GradedLieConformalAlgebrasCategory

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

EXAMPLES:

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

class Super(base_category)

Bases: SuperModulesCategory

The category of super finitely generated Lie conformal algebras with basis.

EXAMPLES:

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

class Graded(base_category)

Bases: GradedModulesCategory

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

EXAMPLES:

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

class Graded(base_category)

Bases: GradedLieConformalAlgebrasCategory

The category of H-graded Lie conformal algebras with basis.

EXAMPLES:

sage: LieConformalAlgebras(QQbar).WithBasis().Graded()                      # needs sage.rings.number_field
Category of H-graded Lie conformal algebras with basis over Algebraic Field

class Super(base_category)

Bases: SuperModulesCategory

The category of super Lie conformal algebras with basis.

EXAMPLES:

sage: LieConformalAlgebras(AA).WithBasis().Super()                          # needs sage.rings.number_field
Category of super Lie conformal algebras with basis
 over Algebraic Real Field

class Graded(base_category)

Bases: GradedLieConformalAlgebrasCategory

The category of H-graded super Lie conformal algebras with basis.

EXAMPLES:

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

class ParentMethods

Bases: object