Theorems · Definition · nonassociative algebras

LieAlgebra.Extension.L

{R : Type u_1} →
  {N : Type u_2} →
    {M : Type u_4} →
      [inst : CommRing R] →
        [inst_1 : LieRing N] →
          [inst_2 : LieAlgebra R N] →
            [inst_3 : LieRing M] → [inst_4 : LieAlgebra R M] → LieAlgebra.Extension R N M → Type u_5

The middle object in the sequence.

Defined in: Mathlib.Algebra.Lie.Extension
Cited by: 21 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CommRing LieRing LieAlgebra LieRing LieAlgebra

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

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
LieAlgebra.Extensionstatement and proof · cited by 20

Cited by27

Results whose statement or proof uses this declaration.

LieAlgebra.Extension.projstatement · cited by 19
LieAlgebra.Extension.inclstatement · cited by 10
LieAlgebra.Extension.toKerstatement and proof · cited by 8
LieAlgebra.Extension.proj_surjectivestatement · cited by 4
LieAlgebra.Extension.twoCocycleOfstatement and proof · cited by 3
LieAlgebra.Extension.lieModuleOfproof · cited by 3
LieAlgebra.Extension.oneCochainOfTwoSplittingstatement and proof · cited by 3
LieAlgebra.Extension.ringModuleOf_bracketstatement · cited by 2
LieAlgebra.Extension.ringModuleOf_bracket_projstatement and proof · cited by 1
LieAlgebra.Extension.twoCocycleOf_coe_coestatement and proof · cited by 1
LieAlgebra.Extension.incl_apply_mem_kerstatement · cited by 1
LieAlgebra.Extension.lie_toKer_applystatement and proof · cited by 1