Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton
∀ {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.corootSpace ⇑α) = K ∙ LieAlgebra.IsKilling.coroot α- Defined in
- Mathlib.Algebra.Lie.Weights.Killing
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Moduleproof · cited by 20,661
- AddCommMonoidproof · cited by 12,281
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- FiniteDimensionalstatement and proof · cited by 1,854
- IsUnitproof · cited by 1,602
- LieRingstatement and proof · cited by 1,548
- Submodule.spanstatement and proof · cited by 1,504
- LinearEquiv.symmproof · cited by 1,461
Cited by7
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_supproof · cited by 3
- LieAlgebra.IsKilling.biSup_corootSpace_eq_topproof · cited by 2
- LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_corootproof · cited by 2
- LieAlgebra.IsKilling.eq_coroot_of_mem_corootSpace_of_twoproof · cited by 1
- LieIdeal.restr_inf_cartan_eq_biSup_corootSubmoduleproof · cited by 1
- LieAlgebra.IsKilling.isCompl_ker_weight_span_corootproof · cited by 0
- LieAlgebra.IsKilling.corootSpace_eq_bot_iffproof · cited by 0