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Theorems · Theorem · nonassociative algebras

LieAlgebra.isSimple_iff_of_not_isLieAbelian

∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],
  ¬IsLieAbelian L → (IsSimpleOrder (LieIdeal R L) ↔ LieAlgebra.IsSimple R L)
Defined in
Mathlib.Algebra.Lie.Semisimple.Basic
Cited by
1 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingLieRingLieAlgebra
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Around this declaration

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

LieAlgebra.IsKilling.isSimple_iff_isIrreducible · cited by 0IsKilling.isSimple_iff_is…CommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieIdeal · cited by 282LieIdealIsLieAbelian · cited by 55IsLieAbelianIsSimpleOrder · cited by 54IsSimpleOrderIsSimpleOrder.eq_bot_or_eq_top · cited by 32IsSimpleOrder.eq_bot_or_e…LieAlgebra.IsSimple · cited by 10LieAlgebra.IsSimpleLieAlgebra.isSimple_iff_of_no…CITED BYCITES

Cites8

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Cited by1

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