Theorems · Theorem · nonassociative algebras

LieModule.traceForm_genWeightSpace_eq

∀ (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] [IsDomain R] [IsPrincipalIdealRing R] [inst_10 : LieRing.IsNilpotent L] [IsNoetherian R M]
  [LieModule.LinearWeights R L M] (χ : L → R) (x y : L),
  ((LieModule.traceForm R L ↥(LieModule.genWeightSpace M χ)) x) y =
    Module.finrank R ↥(LieModule.genWeightSpace M χ) • (χ x * χ y)

Defined in: Mathlib.Algebra.Lie.TraceForm
Cited by: 1 results in Mathlib
Foundations: Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra AddCommGroup Module LieRingModule LieModule Module.Free IsDomain IsPrincipalIdealRing LieRing.IsNilpotent IsNoetherian LieModule.LinearWeights

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Cites52

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
mul_commproof · cited by 2,262
IsDomainstatement and proof · cited by 2,196
Module.finrankstatement and proof · cited by 1,770
LinearMap.compproof · cited by 1,642
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246

Cited by1

Results whose statement or proof uses this declaration.

LieModule.traceForm_eq_sum_finrank_nsmul_mulproof · cited by 1