Theorems · Theorem · nonassociative algebras
LieSubmodule.traceForm_eq_of_le_idealizer
∀ {R : Type u_1} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
[Module.Free R M] [Module.Finite R M] [IsDomain R] [IsPrincipalIdealRing R] (N : LieSubmodule R L M),
∀ I ≤ N.idealizer,
LieModule.traceForm R ↥I ↥N = (LieModule.traceForm R L M).restrict (LieIdeal.toLieSubalgebra R L I).toSubmodule- Defined in
- Mathlib.Algebra.Lie.TraceForm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- IsDomainstatement and proof · cited by 2,196
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Finitestatement and proof · cited by 1,032
- LieRingModulestatement and proof · cited by 727
- Module.Freestatement and proof · cited by 597
- LinearMap.BilinFormstatement · cited by 501
- LieSubmodulestatement and proof · cited by 489
Cited by1
Results whose statement or proof uses this declaration.
- LieIdeal.killingForm_eqproof · cited by 1