Finitely Generated Lambda bracket Algebras#
AUTHORS:
Reimundo Heluani (2020-08-21): Initial implementation.
- class sage.categories.finitely_generated_lambda_bracket_algebras.FinitelyGeneratedLambdaBracketAlgebras(base_category)#
Bases:
CategoryWithAxiom_over_base_ring
The category of finitely generated lambda bracket algebras.
EXAMPLES:
sage: from sage.categories.lambda_bracket_algebras import LambdaBracketAlgebras sage: LambdaBracketAlgebras(QQbar).FinitelyGenerated() # optional - sage.rings.number_field Category of finitely generated lambda bracket 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() # optional - sage.rings.number_field Category of H-graded finitely generated lie conformal algebras over Algebraic Field
- class ParentMethods#
Bases:
object
- gen(i)#
The
i
-th generator of this Lie conformal algebra.EXAMPLES:
sage: V = lie_conformal_algebras.Affine(QQ, 'A1') # optional - sage.combinat sage.modules sage: V.gens() # optional - sage.combinat sage.modules (B[alpha[1]], B[alphacheck[1]], B[-alpha[1]], B['K']) sage: V.gen(0) # optional - sage.combinat sage.modules B[alpha[1]] sage: V.1 # optional - sage.combinat sage.modules B[alphacheck[1]]
- ngens()#
The number of generators of this Lie conformal algebra.
EXAMPLES:
sage: Vir = lie_conformal_algebras.Virasoro(QQ) # optional - sage.combinat sage.modules sage: Vir.ngens() # optional - sage.combinat sage.modules 2 sage: V = lie_conformal_algebras.Affine(QQ, 'A2') # optional - sage.combinat sage.modules sage: V.ngens() # optional - sage.combinat sage.modules 9
- some_elements()#
Some elements of this Lie conformal algebra.
This method returns a list with elements containing at least the generators.
EXAMPLES:
sage: V = lie_conformal_algebras.Affine(QQ, 'A1', # optional - sage.combinat sage.modules ....: names=('e', 'h', 'f')) sage: V.some_elements() # optional - sage.combinat sage.modules [e, h, f, K, ...] sage: all(v.parent() is V for v in V.some_elements()) # optional - sage.combinat sage.modules True