Theorems · Theorem · nonassociative algebras
LieIdeal.coe_bracket_of_module
∀ (M : Type w) [inst : AddCommGroup M] {R : Type u_1} {L : Type u_2} [inst_1 : CommRing R] [inst_2 : LieRing L]
[inst_3 : LieAlgebra R L] (I : LieIdeal R L) [inst_4 : LieRingModule L M] (x : ↥I) (m : M), ⁅x, m⁆ = ⁅↑x, m⁆- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement · cited by 642
- LieIdealstatement and proof · cited by 282
- LieIdeal.toLieSubalgebraproof · cited by 48
- LieSubalgebra.coe_bracket_of_moduleproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- LieModule.exists_nontrivial_weightSpace_of_lieIdealproof · cited by 0
- LieIdeal.isLieAbelian_iffproof · cited by 0
- LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplittingproof · cited by 0