Theorems · Theorem · nonassociative algebras
LieDerivation.IsKilling.exists_eq_ad
∀ {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] (D : LieDerivation R L L), ∃ x, (LieDerivation.ad R L) x = DEvery derivation of a finite-dimensional Killing Lie algebra is an inner derivation.
- Defined in
- Mathlib.Algebra.Lie.Derivation.Killing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Finitestatement and proof · cited by 1,032
- LieSubalgebraproof · cited by 418
- LieHomstatement · cited by 382
- LieAlgebra.IsKillingstatement and proof · cited by 122
- LieDerivationstatement and proof · cited by 95
- Submodule.mem_topproof · cited by 58
- LieDerivation.adstatement · cited by 19
- LieDerivation.IsKilling.range_ad_eq_topproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1