Theorems · Theorem · nonassociative algebras

LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe

∀ (R : Type u_1) (A : Type u_2) (L : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : CommRing A] [inst_4 : IsAddTorsionFree R] [inst_5 : Algebra A R] (Φ : LinearMap.BilinForm R L)
  (hΦ : LinearMap.BilinForm.lieInvariant L Φ) (hΦs : Φ.IsSymm),
  ↑(LieAlgebra.LoopAlgebra.twoCocycleOfBilinear R A L Φ hΦ hΦs) =
    LieAlgebra.LoopAlgebra.twoCochainOfBilinear R A L Φ hΦs

Defined in: Mathlib.Algebra.Lie.Loop
Cited by: 0 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra CommRing IsAddTorsionFree Algebra

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RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
LinearMapstatement · cited by 10,215
Submodulestatement · cited by 7,192
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
AddMonoidAlgebrastatement · cited by 649
LinearMap.BilinFormstatement and proof · cited by 501
IsAddTorsionFreestatement and proof · cited by 155
LieModule.Cohomology.twoCochainstatement · cited by 38
LinearMap.BilinForm.IsSymmstatement and proof · cited by 35

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