例句與造句

1. Note that for reductive Lie algebras, the Cartan subalgebra is required to contain the center.
2. This is the approach followed in, for instance, which classifies representations of split semisimple / reductive Lie algebras.
3. The intersection of reductive Lie algebras and solvable Lie algebras is exactly abelian Lie algebras ( contrast with the intersection of semisimple and solvable Lie algebras being trivial ).
4. In characteristic 0, every reductive Lie algebra ( one that is a sum of abelian and simple Lie algebras ) has a non-degenerate invariant symmetric bilinear form.
5. Any two splitting Cartan algebras are conjugate, and they fulfill a similar function to Cartan algebras in semisimple Lie algebras over algebraically closed fields, so split semisimple Lie algebras ( indeed, split reductive Lie algebras ) share many properties with semisimple Lie algebras over algebraically closed fields.
6. It's difficult to find reductive lie algebra in a sentence. 用reductive lie algebra造句挺難的
7. In the mathematical fields of Lie theory and algebraic topology, the notion of "'Cartan pair "'is a technical condition on the relationship between a reductive Lie algebra \ mathfrak { g } and a subalgebra \ mathfrak { k } reductive in \ mathfrak { g }.
8. Many properties of complex semisimple / reductive Lie algebras are true not only for semisimple / reductive Lie algebras over algebraically closed fields, but more generally for split semisimple / reductive Lie algebras over other fields : semisimple / reductive Lie algebras over algebraically closed fields are always split, but over other fields this is not always the case.
9. Many properties of complex semisimple / reductive Lie algebras are true not only for semisimple / reductive Lie algebras over algebraically closed fields, but more generally for split semisimple / reductive Lie algebras over other fields : semisimple / reductive Lie algebras over algebraically closed fields are always split, but over other fields this is not always the case.
10. Many properties of complex semisimple / reductive Lie algebras are true not only for semisimple / reductive Lie algebras over algebraically closed fields, but more generally for split semisimple / reductive Lie algebras over other fields : semisimple / reductive Lie algebras over algebraically closed fields are always split, but over other fields this is not always the case.
11. Many properties of complex semisimple / reductive Lie algebras are true not only for semisimple / reductive Lie algebras over algebraically closed fields, but more generally for split semisimple / reductive Lie algebras over other fields : semisimple / reductive Lie algebras over algebraically closed fields are always split, but over other fields this is not always the case.
12. Split Lie algebras are of interest both because they formalize the split real form of a complex Lie algebra, and because split semisimple Lie algebras ( more generally, split reductive Lie algebras ) over any field share many properties with semisimple Lie algebras over algebraically closed fields  having essentially the same representation theory, for instance  the splitting Cartan subalgebra playing the same role as the Cartan subalgebra plays over algebraically closed fields.