Mathlib Map

Theorems · Theorem · nonassociative algebras

LieModule.traceForm_eq_zero_of_isNilpotent

∀ (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] [IsReduced R]
  [LieModule.IsNilpotent L M], LieModule.traceForm R L M = 0
Defined in
Mathlib.Algebra.Lie.TraceForm
Cited by
1 results in Mathlib
Foundations
Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleIsReducedLieModule.IsNilpotent
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieModule.traceForm_genWeightSpace_eq · cited by 1LieModule.traceForm_genWe…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupLinearMap · cited by 10215LinearMapLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieRingModule · cited by 727LieRingModuleLinearMap.BilinForm · cited by 501LinearMap.BilinFormLieModule · cited by 424LieModuleIsReduced · cited by 98IsReducedLieModule.IsNilpotent · cited by 46LieModule.IsNilpotentLieModule.traceForm · cited by 41LieModule.traceFormLinearMap.BilinForm.ext · cited by 22BilinForm.extLinearMap.isNilpotent_trace_of_isNilpotent · cited by 5LinearMap.isNilpotent_tra…LieModule.traceForm_eq_zero_o…CITED BYCITES

Cites16

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

Cited by1

Results whose statement or proof uses this declaration.