AUTHORS:

• Eero Hakavuori (2018-08-16): initial version

class Stratified(base_category)

Category of stratified Lie algebras.

A graded Lie algebra $$L = \bigoplus_{k=1}^M L_k$$ (where possibly $$M = \infty$$) is called stratified if it is generated by $$L_1$$; in other words, we have $$L_{k+1} = [L_1, L_k]$$.

class FiniteDimensional(base_category)

Category of finite dimensional stratified Lie algebras.

EXAMPLES:

Category of finite dimensional stratified Lie algebras over Rational Field
extra_super_categories()

Implements the fact that a finite dimensional stratified Lie algebra is nilpotent.

EXAMPLES:

sage: C.extra_super_categories()
[Category of nilpotent Lie algebras over Rational Field]
sage: C is C.Nilpotent()
True
sage: C.is_subcategory(LieAlgebras(QQ).Nilpotent())
True
class SubcategoryMethods
Stratified()

Return the full subcategory of stratified objects of self.

A Lie algebra is stratified if it is graded and generated as a Lie algebra by its component of degree one.

EXAMPLES: