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