Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.span_weight_isNonZero_eq_top
∀ (K : Type u_2) (L : Type u_3) [inst : LieRing L] [inst_1 : Field K] [inst_2 : LieAlgebra K L]
[inst_3 : FiniteDimensional K L] (H : LieSubalgebra K L) [inst_4 : H.IsCartanSubalgebra]
[inst_5 : LieAlgebra.IsKilling K L] [LieModule.IsTriangularizable K (↥H) L],
Submodule.span K (LieModule.Weight.toLinear K (↥H) L '' {α | α.IsNonZero}) = ⊤- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- LinearMapstatement and proof · cited by 10,215
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Set.ofPredstatement and proof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Set.rangeproof · cited by 4,705
- le_antisymmproof · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- LieRingstatement and proof · cited by 1,548
- Submodule.spanstatement and proof · cited by 1,504
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.