Theorems · Theorem · nonassociative algebras

LieModule.traceForm_eq_sum_finrank_nsmul_mul

∀ (K : Type u_2) (L : Type u_3) (M : Type u_4) [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M]
  [inst_3 : Field K] [inst_4 : LieAlgebra K L] [inst_5 : Module K M] [inst_6 : LieModule K L M]
  [inst_7 : FiniteDimensional K M] [inst_8 : LieRing.IsNilpotent L] [LieModule.LinearWeights K L M]
  [LieModule.IsTriangularizable K L M] (x y : L),
  ((LieModule.traceForm K L M) x) y = ∑ χ, Module.finrank K ↥(LieModule.genWeightSpace M ⇑χ) • (χ x * χ y)

Defined in: Mathlib.Algebra.Lie.TraceForm
Cited by: 1 results in Mathlib
Foundations: Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LieRing AddCommGroup LieRingModule Field LieAlgebra Module LieModule FiniteDimensional LieRing.IsNilpotent LieModule.LinearWeights LieModule.IsTriangularizable

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
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LinearMapstatement · cited by 10,215
SetLike.coeproof · cited by 8,199
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Finset.univstatement and proof · cited by 3,473
Finset.sum_congrproof · cited by 2,323
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankstatement and proof · cited by 1,770

Cited by1

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LieModule.traceForm_eq_sum_finrank_nsmulproof · cited by 2