Theorems · Theorem · nonassociative algebras
LieModule.traceForm_isSymm
∀ (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], LinearMap.IsSymm (LieModule.traceForm R L M)
- Defined in
- Mathlib.Algebra.Lie.TraceForm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LieModulestatement and proof · cited by 424
- LinearMap.IsSymmstatement · cited by 48
- LieModule.traceFormstatement · cited by 41
- LieModule.traceForm_commproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.killingForm_nondegenerateproof · cited by 2
- LieDerivation.IsKilling.range_ad_eq_topproof · cited by 1
- LieAlgebra.IsKilling.traceForm_cartan_nondegenerateproof · cited by 0
- LieIdeal.isCompl_killingComplproof · cited by 0