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Theorems · Theorem · nonassociative algebras

LieAlgebra.Basis.isLieAbelian_cartan

∀ {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} (b : LieAlgebra.Basis ι H), IsLieAbelian ↥H
Defined in
Mathlib.Algebra.Lie.Basis.Basic
Cited by
7 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FiniteCommRingLieRingLieAlgebra
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Around this declaration

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

LieAlgebra.Basis.isCartanSubalgebra · cited by 6Basis.isCartanSubalgebraLieAlgebra.Basis.iSupIndep_rootSpace · cited by 3Basis.iSupIndep_rootSpaceLieAlgebra.Basis.cartan_eq · cited by 2Basis.cartan_eqLieAlgebra.Basis.borelLower_eq · cited by 1Basis.borelLower_eqLieAlgebra.Basis.borelUpper_eq · cited by 1Basis.borelUpper_eqLieAlgebra.Basis.borelUpper_le_biSup · cited by 1Basis.borelUpper_le_biSupLieAlgebra.Basis.borelLower_le_biSup · cited by 0Basis.borelLower_le_biSupCommRing · cited by 17173CommRingSet.range · cited by 4705Set.rangeFinite · cited by 3029FiniteLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieSubalgebra · cited by 418LieSubalgebraIsLieAbelian · cited by 55IsLieAbelianLieAlgebra.Basis · cited by 44LieAlgebra.BasisLieAlgebra.Basis.h · cited by 17Basis.hLieAlgebra.Basis.cartan_eq_lieSpan · cited by 3Basis.cartan_eq_lieSpanLieAlgebra.Basis.lie_h_h · cited by 2Basis.lie_h_hLieSubalgebra.isLieAbelian_lieSpan_iff · cited by 1LieSubalgebra.isLieAbelia…Basis.isLieAbelian_cartanCITED BYCITES

Cites12

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Cited by7

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