Finitely Generated Lie Conformal Algebras¶
AUTHORS:
- Reimundo Heluani (2019-10-05): Initial implementation. 
- class sage.categories.finitely_generated_lie_conformal_algebras.FinitelyGeneratedLieConformalAlgebras(base_category)[source]¶
- 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 - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).FinitelyGenerated() # needs sage.rings.number_field Category of finitely generated Lie conformal algebras over Algebraic Field - class Graded(base_category)[source]¶
- 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 - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).FinitelyGenerated().Graded() # needs sage.rings.number_field Category of H-graded finitely generated Lie conformal algebras over Algebraic Field 
 - class ParentMethods[source]¶
- Bases: - object- some_elements()[source]¶
- 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 - >>> from sage.all import * >>> V = lie_conformal_algebras.Affine(QQ, 'A1', # needs sage.combinat sage.modules ... names=('e', 'h', 'f')) >>> V.some_elements() # needs sage.combinat sage.modules [e, h, f, K, ...] >>> all(v.parent() is V for v in V.some_elements()) # needs sage.combinat sage.modules True 
 
 - class Super(base_category)[source]¶
- 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 - >>> from sage.all import * >>> 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)[source]¶
- 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 - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).FinitelyGenerated().Super().Graded() # needs sage.rings.number_field Category of H-graded super finitely generated Lie conformal algebras over Algebraic Field