Theorems · Definition · nonassociative algebras
LieAlgebra.center
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieIdeal R L
The center of a Lie algebra is the set of elements that commute with everything. It can be viewed as the maximal trivial submodule of the Lie algebra as a Lie module over itself via the adjoint representation.
- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LieIdealstatement · cited by 282
- LieModule.maxTrivSubmoduleproof · cited by 25
Cited by25
Results whose statement or proof uses this declaration.
- LieAlgebra.center_eq_botstatement · cited by 3
- LieAlgebra.self_module_ker_eq_centerstatement and proof · cited by 3
- LieDerivation.ad_ker_eq_centerstatement and proof · cited by 3
- LieAlgebra.center_le_radicalstatement and proof · cited by 2
- LieAlgebra.isLieAbelian_iff_center_eq_topstatement · cited by 2
- LieAlgebra.nilpotent_of_nilpotent_quotientstatement and proof · cited by 1
- LieAlgebra.HasCentralRadical.casesOnstatement and proof · cited by 1
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulstatement and proof · cited by 1
- LieAlgebra.hasCentralRadical_iffstatement and proof · cited by 1
- LieAlgebra.isFaithful_self_iffstatement and proof · cited by 1
- LieModule.lowerCentralSeries_one_inf_center_le_ker_traceFormstatement and proof · cited by 1
- LieModule.commute_toEnd_of_mem_center_leftstatement and proof · cited by 1