Theorems · Definition · nonassociative algebras
LieAlgebra.ad
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → L →ₗ⁅R⁆ Module.End R L
The adjoint action of a Lie algebra on itself.
- Defined in
- Mathlib.Algebra.Lie.OfAssociative
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Endstatement · cited by 774
- LieHomstatement · cited by 382
- LieRing.ofAssociativeRingstatement · cited by 227
- LieModule.toEndproof · cited by 144
Cited by52
Results whose statement or proof uses this declaration.
- LieSubalgebra.engelproof · cited by 13
- LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpaceproof · cited by 8
- LieSubalgebra.mem_engel_iffstatement and proof · cited by 4
- LieSubalgebra.self_mem_engelproof · cited by 4
- LieAlgebra.ad_eq_lmul_left_sub_lmul_rightstatement · cited by 3
- LieSubalgebra.isNilpotent_ad_of_isNilpotent_adstatement and proof · cited by 2
- LieModule.toEnd_liestatement · cited by 2
- LieAlgebra.finrank_engelstatement and proof · cited by 2
- LieAlgebra.isNilpotent_iff_forallstatement · cited by 2
- LieAlgebra.ad_nilpotent_of_nilpotentstatement · cited by 2
- LieAlgebra.commute_ad_of_commutestatement and proof · cited by 1
- LieSubalgebra.isNilpotent_of_forall_le_engelproof · cited by 1