Theorems · Theorem · nonassociative algebras
LieAlgebra.IsKilling.killingForm_nondegenerate
∀ (R : Type u_1) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [LieAlgebra.IsKilling R L], (killingForm R L).Nondegenerate
- Defined in
- Mathlib.Algebra.Lie.Killing
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 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.
- CommRingstatement and proof · cited by 17,173
- Bot.botproof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieAlgebra.IsKillingstatement and proof · cited by 122
- LinearMap.BilinForm.Nondegeneratestatement · cited by 77
- killingFormstatement · cited by 34
- LinearMap.IsSymm.isReflproof · cited by 11
- LinearMap.IsRefl.nondegenerate_iff_separatingLeftproof · cited by 9
- LieAlgebra.IsKilling.ker_killingForm_eq_botproof · cited by 7
- LieModule.traceForm_isSymmproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LieDerivation.IsKilling.killingForm_restrict_range_ad_nondegenerateproof · cited by 1
- LieIdeal.isCompl_killingComplproof · cited by 0