Graded Lie Algebras With Basis

class sage.categories.graded_lie_algebras_with_basis.GradedLieAlgebrasWithBasis(base_category)

Bases: GradedModulesCategory

The category of graded Lie algebras with a distinguished basis.

EXAMPLES:

Sage

sage: C = LieAlgebras(ZZ).WithBasis().Graded(); C
Category of graded Lie algebras with basis over Integer Ring
sage: C.super_categories()
[Category of graded modules with basis over Integer Ring,
 Category of Lie algebras with basis over Integer Ring,
 Category of graded Lie algebras over Integer Ring]

sage: C is LieAlgebras(ZZ).WithBasis().Graded()
True
sage: C is LieAlgebras(ZZ).Graded().WithBasis()
False

Python

>>> from sage.all import *
>>> C = LieAlgebras(ZZ).WithBasis().Graded(); C
Category of graded Lie algebras with basis over Integer Ring
>>> C.super_categories()
[Category of graded modules with basis over Integer Ring,
 Category of Lie algebras with basis over Integer Ring,
 Category of graded Lie algebras over Integer Ring]

>>> C is LieAlgebras(ZZ).WithBasis().Graded()
True
>>> C is LieAlgebras(ZZ).Graded().WithBasis()
False

FiniteDimensional

alias of FiniteDimensionalGradedLieAlgebrasWithBasis