Lambda Bracket Algebras With Basis

AUTHORS:

• Reimundo Heluani (2020-08-21): Initial implementation.

class sage.categories.lambda_bracket_algebras_with_basis.LambdaBracketAlgebrasWithBasis(base_category)

Bases: CategoryWithAxiom_over_base_ring

The category of Lambda bracket algebras with basis.

EXAMPLES:

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

class ElementMethods

Bases: object

index()

The index of this basis element.

EXAMPLES:

sage: V = lie_conformal_algebras.NeveuSchwarz(QQ)                       # optional - sage.combinat sage.modules
sage: V.inject_variables()                                              # optional - sage.combinat sage.modules
Defining L, G, C
sage: G.T(3).index()                                                    # optional - sage.combinat sage.modules
('G', 3)
sage: v = V.an_element(); v                                             # optional - sage.combinat sage.modules
L + G + C
sage: v.index()                                                         # optional - sage.combinat sage.modules
Traceback (most recent call last):
...
ValueError: index can only be computed for monomials, got L + G + C

class FinitelyGeneratedAsLambdaBracketAlgebra(base_category)

Bases: CategoryWithAxiom_over_base_ring

The category of finitely generated lambda bracket algebras with basis.

EXAMPLES:

sage: C = LieConformalAlgebras(QQbar)                                      # optional - sage.rings.number_field
sage: C1 = C.WithBasis().FinitelyGenerated(); C1                           # optional - sage.rings.number_field
Category of finitely generated Lie conformal algebras with basis
 over Algebraic Field
sage: C2 = C.FinitelyGenerated().WithBasis(); C2                           # optional - sage.rings.number_field
Category of finitely generated Lie conformal algebras with basis
 over Algebraic Field
sage: C1 is C2                                                             # optional - sage.rings.number_field
True

class Graded(base_category)

Bases: GradedModulesCategory

The category of H-graded finitely generated lambda bracket algebras with basis.

EXAMPLES:

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

class ParentMethods

Bases: object

degree_on_basis(m)

Return the degree of the basis element indexed by m in self.

EXAMPLES:

sage: V = lie_conformal_algebras.Virasoro(QQ)                   # optional - sage.combinat sage.modules
sage: V.degree_on_basis(('L', 2))                               # optional - sage.combinat sage.modules
4