Finite Dimensional Graded Lie Algebras With Basis

AUTHORS:

  • Eero Hakavuori (2018-08-16): initial version
sage.categories.finite_dimensional_graded_lie_algebras_with_basis.FiniteDimensionalGradedLieAlgebrasWithBasis

Category of finite dimensional graded Lie algebras with a basis.

A grading of a Lie algebra \(\mathfrak{g}\) is a direct sum decomposition \(\mathfrak{g} = \bigoplus_{i} V_i\) such that \([V_i,V_j] \subset V_{i+j}\).

EXAMPLES:

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

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