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