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()
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)
sage: V.inject_variables()
Defining L, G, C
sage: G.T(3).index()
('G', 3)
sage: v = V.an_element(); v
L + G + C
sage: v.index()
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)
sage: C.WithBasis().FinitelyGenerated()
Category of finitely generated Lie conformal algebras with basis over Algebraic Field
sage: C.WithBasis().FinitelyGenerated() is C.FinitelyGenerated().WithBasis()
True

class Graded(base_category)

Bases: GradedModulesCategory

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

EXAMPLES:

sage: LieConformalAlgebras(QQbar).WithBasis().FinitelyGenerated().Graded()
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)
sage: V.degree_on_basis(('L',2))
4