Mathlib Map

Theorems · Definition · nonassociative algebras

LieSubalgebra.toSubmodule

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieSubalgebra R L → Submodule R L
Defined in
Mathlib.Algebra.Lie.Subalgebra
Cited by
90 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
CommRingLieRingLieAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieIdeal.map · cited by 33LieIdeal.mapLieSubalgebra.toLieSubmodule · cited by 26LieSubalgebra.toLieSubmod…LieIdeal.comap · cited by 21LieIdeal.comapLieAlgebra.Basis.baseSupp · cited by 15Basis.baseSuppLieSubalgebra.map · cited by 14LieSubalgebra.mapLieAlgebra.rootSpace_zero_eq · cited by 9LieAlgebra.rootSpace_zero…LieAlgebra.IsKilling.sl2SubmoduleOfRoot · cited by 9IsKilling.sl2SubmoduleOfR…LieSubalgebra.toSubmodule_inj · cited by 8LieSubalgebra.toSubmodule…LieAlgebra.IsKilling.ker_killingForm_eq_bot · cited by 7IsKilling.ker_killingForm…LieSubalgebra.incl · cited by 7LieSubalgebra.inclLieSubalgebra.coe_toLieSubmodule · cited by 6LieSubalgebra.coe_toLieSu…LieSubalgebra.inclusion · cited by 6LieSubalgebra.inclusionLieAlgebra.Basis.borelUpper · cited by 5Basis.borelUpperLieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero · cited by 5IsKilling.exists_isSl2Tri…LieIdeal.toLieSubalgebra_toSubmodule · cited by 5LieIdeal.toLieSubalgebra_…CommRing · cited by 17173CommRingSubmodule · cited by 7192SubmoduleLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieSubalgebra · cited by 418LieSubalgebraLieSubalgebra.toSubmoduleCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by110

Results whose statement or proof uses this declaration.