Theorems · Theorem · nonassociative algebras
LieModule.traceForm_comm
∀ (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] (x y : L), ((LieModule.traceForm R L M) x) y = ((LieModule.traceForm R L M) y) x
- Defined in
- Mathlib.Algebra.Lie.TraceForm
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LinearMap.BilinFormstatement · cited by 501
- LieModulestatement and proof · cited by 424
- LieModule.toEndproof · cited by 144
Cited by9
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- LieModule.traceForm_isSymmproof · cited by 5
- LieAlgebra.IsKilling.orthogonal_span_coroot_eq_kerproof · cited by 2
- LieAlgebra.isKilling_of_equivproof · cited by 1
- LieModule.traceForm_flipproof · cited by 1
- LieAlgebra.killingCompl_top_le_radicalproof · cited by 0
- LieIdeal.coe_killingCompl_topproof · cited by 0
- LieIdeal.isCompl_killingComplproof · cited by 0