Theorems · Theorem · nonassociative algebras
LieAlgebra.le_zeroRootSubalgebra
∀ (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 : LieRing.IsNilpotent ↥H], H ≤ LieAlgebra.zeroRootSubalgebra R L H
- Defined in
- Mathlib.Algebra.Lie.Weights.Cartan
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 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
- LieSubalgebrastatement and proof · cited by 418
- LieRing.IsNilpotentstatement and proof · cited by 176
- LieSubmodule.toSubmoduleproof · cited by 150
- LieSubalgebra.toSubmoduleproof · cited by 90
- LieAlgebra.rootSpaceproof · cited by 74
- LieSubalgebra.toLieSubmoduleproof · cited by 26
- LieAlgebra.zeroRootSubalgebrastatement and proof · cited by 10
- LieSubalgebra.coe_toLieSubmoduleproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.zeroRootSubalgebra_eq_of_is_cartanproof · cited by 2
- LieAlgebra.zeroRootSubalgebra_normalizer_eq_selfproof · cited by 1
- LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebraproof · cited by 1