Lie Conformal Algebras With Basis¶
AUTHORS:
- Reimundo Heluani (2019-10-05): Initial implementation. 
- class sage.categories.lie_conformal_algebras_with_basis.LieConformalAlgebrasWithBasis(base_category)[source]¶
- 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 - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).WithBasis() # needs sage.rings.number_field Category of Lie conformal algebras with basis over Algebraic Field - class FinitelyGeneratedAsLambdaBracketAlgebra(base_category)[source]¶
- 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 - >>> from sage.all import * >>> C = LieConformalAlgebras(QQbar) # needs sage.rings.number_field >>> CWF = C.WithBasis().FinitelyGenerated(); CWF # needs sage.rings.number_field Category of finitely generated Lie conformal algebras with basis over Algebraic Field >>> CWF is C.FinitelyGenerated().WithBasis() # needs sage.rings.number_field True - class Graded(base_category)[source]¶
- 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 - >>> from sage.all import * >>> 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)[source]¶
- 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 - >>> from sage.all import * >>> 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)[source]¶
- 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 - >>> from sage.all import * >>> C = LieConformalAlgebras(QQbar).WithBasis().FinitelyGenerated() # needs sage.rings.number_field >>> C.Graded().Super() # needs sage.rings.number_field Category of H-graded super finitely generated Lie conformal algebras with basis over Algebraic Field >>> C.Graded().Super() is C.Super().Graded() # needs sage.rings.number_field True 
 
 
 - class Graded(base_category)[source]¶
- 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 - >>> from sage.all import * >>> 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)[source]¶
- 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 - >>> from sage.all import * >>> 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)[source]¶
- 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 - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).WithBasis().Super().Graded() # needs sage.rings.number_field Category of H-graded super Lie conformal algebras with basis over Algebraic Field