Theorems · Theorem · nonassociative algebras
LieDerivation.IsKilling.ad_apply_eq_zero_iff
∀ (R : Type u_1) (L : Type u_2) [inst : Field R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [Module.Finite R L] [LieAlgebra.IsKilling R L] (x : L), (LieDerivation.ad R L) x = 0 ↔ x = 0
- Defined in
- Mathlib.Algebra.Lie.Derivation.Killing
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Fieldstatement and proof · cited by 7,404
- map_zeroproof · cited by 1,614
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Finitestatement and proof · cited by 1,032
- LieHomstatement · cited by 382
- LieIdealproof · cited by 282
- LieAlgebra.IsKillingstatement and proof · cited by 122
- LieDerivationstatement · cited by 95
- LieDerivation.adstatement and proof · cited by 19
- LieSubmodule.mem_botproof · cited by 11
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.