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Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.cartan_eq_lieSpan

∀ {ι : Type u_1} {R : Type u_2} {L : Type u_3} [inst : Finite ι] [inst_1 : CommRing R] [inst_2 : LieRing L]
  [inst_3 : LieAlgebra R L] {H : LieSubalgebra R L} (self : LieAlgebra.Basis ι H),
  H = LieSubalgebra.lieSpan R L (Set.range self.h)
Defined in
Mathlib.Algebra.Lie.Basis.Basic
Cited by
3 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
FiniteCommRingLieRingLieAlgebra
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Around this declaration

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

LieAlgebra.Basis.isLieAbelian_cartan · cited by 7Basis.isLieAbelian_cartanLieAlgebra.Basis.coe_cartan_eq_span · cited by 4Basis.coe_cartan_eq_spanLieAlgebra.Basis.coroot_eq_h' · cited by 1Basis.coroot_eq_h'CommRing · cited by 17173CommRingSet.range · cited by 4705Set.rangeFinite · cited by 3029FiniteLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieSubalgebra · cited by 418LieSubalgebraLieAlgebra.Basis · cited by 44LieAlgebra.BasisLieSubalgebra.lieSpan · cited by 33LieSubalgebra.lieSpanLieAlgebra.Basis.h · cited by 17Basis.hBasis.cartan_eq_lieSpanCITED BYCITES

Cites9

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Cited by3

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