Theorems · Theorem · nonassociative algebras
LieSubalgebra.isNonZero_coe_root
∀ {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] (α : ↥LieSubalgebra.root),
(↑α).IsNonZero- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubalgebrastatement and proof · cited by 418
- LieModule.Weightstatement and proof · cited by 172
- LieSubalgebra.IsCartanSubalgebrastatement and proof · cited by 135
- LieModule.Weight.IsNonZerostatement and proof · cited by 47
- LieSubalgebra.rootstatement and proof · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdealproof · cited by 2
- LieIdeal.mem_rootSet_of_mem_rootSpanproof · cited by 1
- LieIdeal.restr_eq_iSup_sl2SubmoduleOfRootstatement and proof · cited by 1
- LieAlgebra.IsKilling.lieIdealOrderIso_left_invproof · cited by 0