Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.coroot_eq_zero_iff
∀ {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] [CharZero K]
{α : LieModule.Weight K (↥H) L}, LieAlgebra.IsKilling.coroot α = 0 ↔ α.IsZero- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- map_zeroproof · cited by 1,614
- LieRingstatement and proof · cited by 1,548
- LinearEquiv.symmproof · cited by 1,461
- LieAlgebrastatement and proof · cited by 1,246
- CharZerostatement and proof · cited by 932
- smul_zeroproof · cited by 665
- LieSubalgebrastatement and proof · cited by 418
- inv_zeroproof · cited by 184
- LieModule.Weightstatement and proof · cited by 172
Cited by6
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.coe_corootSpace_eq_span_singletonproof · cited by 7
- LieAlgebra.IsKilling.apply_coroot_eq_cast'proof · cited by 4
- LieAlgebra.IsKilling.chainLength_nsmulproof · cited by 1
- LieAlgebra.IsKilling.coroot_eq_iffproof · cited by 0
- LieAlgebra.IsKilling.isCompl_ker_weight_span_corootproof · cited by 0
- LieAlgebra.IsKilling.reflectRoot_isNonZeroproof · cited by 0