Theorems · Theorem · nonassociative algebras
LinearMap.BilinForm.lieInvariant_iff
∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] (Φ : LinearMap.BilinForm R M) [inst_5 : LieAlgebra R L]
[inst_6 : LieModule R L M],
LinearMap.BilinForm.lieInvariant L Φ ↔ Φ ∈ LieModule.maxTrivSubmodule R L (LinearMap.BilinForm R M)- Defined in
- Mathlib.Algebra.Lie.InvariantForm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- sub_selfproof · cited by 996
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketproof · cited by 642
- LinearMap.BilinFormstatement and proof · cited by 501
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