Theorems · Theorem · nonassociative algebras
LieAlgebra.rootSpace.congr_simp
∀ {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] (χ χ_1 : ↥H → R),
χ = χ_1 → LieAlgebra.rootSpace H χ = LieAlgebra.rootSpace H χ_1- Defined in
- Mathlib.Algebra.Lie.Weights.Cartan
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubmodulestatement · cited by 489
- LieSubalgebrastatement and proof · cited by 418
- LieRing.IsNilpotentstatement and proof · cited by 176
- LieAlgebra.rootSpacestatement and proof · cited by 74
Cited by8
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_leproof · cited by 3
- LieAlgebra.IsKilling.corootSpace_zero_eq_botproof · cited by 2
- LieAlgebra.IsKilling.rootSpace_two_smulproof · cited by 1
- LieAlgebra.Basis.borelUpper_le_biSupproof · cited by 1
- LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smulproof · cited by 1
- LieAlgebra.Basis.borelLower_le_biSupproof · cited by 0
- LieAlgebra.Basis.root_mem_or_mem_negproof · cited by 0