Theorems · Definition · nonassociative algebras
LieSubalgebra.lieSpan
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → Set L → LieSubalgebra R L
The Lie subalgebra of a Lie algebra L generated by a subset s ⊆ L.
- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- InfSet.sInfproof · cited by 935
- LieSubalgebrastatement and proof · cited by 418
Cited by42
Results whose statement or proof uses this declaration.
- LieSubalgebra.subset_lieSpanstatement · cited by 19
- RootPairing.GeckConstruction.lieAlgebraproof · cited by 14
- LieSubalgebra.lieSpan_inductionstatement and proof · cited by 9
- LieSubalgebra.lieSpan_lestatement and proof · cited by 7
- LieAlgebra.Basis.borelUpperproof · cited by 5
- LieAlgebra.Basis.borelLowerproof · cited by 4
- LieAlgebra.Basis.coe_cartan_eq_spanproof · cited by 4
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- LieAlgebra.Basis.cartan_eq_lieSpanstatement · cited by 3
- LieSubalgebra.gistatement and proof · cited by 3
- LieSubalgebra.mem_lieSpanstatement · cited by 2
- LieAlgebra.Basis.extproof · cited by 2