Theorems · Theorem · nonassociative algebras
LieAlgebra.rootSpace_zero_eq
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (H : LieSubalgebra R L) [inst_3 : H.IsCartanSubalgebra] [IsNoetherian R L], LieAlgebra.rootSpace H 0 = H.toLieSubmodule
- Defined in
- Mathlib.Algebra.Lie.Weights.Cartan
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submoduleproof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubmodulestatement · cited by 489
- LieSubalgebrastatement and proof · cited by 418
- IsNoetherianstatement and proof · cited by 208
- LieSubmodule.toSubmoduleproof · cited by 150
- LieSubalgebra.IsCartanSubalgebrastatement and proof · cited by 135
- LieSubalgebra.toSubmoduleproof · cited by 90
- LieAlgebra.rootSpacestatement and proof · cited by 74
- LieSubmodule.toSubmodule_injproof · cited by 34
Cited by9
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.corootSpace_zero_eq_botproof · cited by 2
- LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdealproof · cited by 2
- LieAlgebra.mem_corootSpace'proof · cited by 2
- LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1
- LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebraproof · cited by 1
- LieAlgebra.lieIdeal_eq_inf_cartan_sup_biSup_inf_rootSpaceproof · cited by 1
- LieAlgebra.Basis.root_mem_or_mem_negproof · cited by 0
- LieAlgebra.cartan_sup_iSup_rootSpace_eq_topproof · cited by 0