Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.iInf_ker_weight_eq_bot
∀ {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], ⨅ α, LieModule.Weight.ker = ⊥- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 2 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- iSupproof · cited by 2,415
- FiniteDimensionalstatement and proof · cited by 1,854
- iInfstatement · cited by 1,690
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Dualproof · cited by 583
- LieSubalgebrastatement and proof · cited by 418
- LieModule.Weightstatement and proof · cited by 172
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.eq_zero_of_apply_eq_zero_of_mem_corootSpaceproof · cited by 1
- LieIdeal.restr_inf_cartan_eq_biSup_corootSubmoduleproof · cited by 1