diff --git a/Mathbin/Algebra/Lie/CartanMatrix.lean b/Mathbin/Algebra/Lie/CartanMatrix.lean index 7fa7ae46f0..db71d460ff 100644 --- a/Mathbin/Algebra/Lie/CartanMatrix.lean +++ b/Mathbin/Algebra/Lie/CartanMatrix.lean @@ -126,24 +126,24 @@ local notation "F" => FreeLieAlgebra.of R ∘ Generators.F local notation "ad" => LieAlgebra.ad R (FreeLieAlgebra R (Generators B)) /-- The terms correpsonding to the `⁅H, H⁆`-relations. -/ -def hH : B × B → FreeLieAlgebra R (Generators B) := +def HH : B × B → FreeLieAlgebra R (Generators B) := uncurry fun i j => ⁅H i, H j⁆ -#align cartan_matrix.relations.HH CartanMatrix.Relations.hH +#align cartan_matrix.relations.HH CartanMatrix.Relations.HH /-- The terms correpsonding to the `⁅E, F⁆`-relations. -/ -def eF : B × B → FreeLieAlgebra R (Generators B) := +def EF : B × B → FreeLieAlgebra R (Generators B) := uncurry fun i j => if i = j then ⁅E i, F i⁆ - H i else ⁅E i, F j⁆ -#align cartan_matrix.relations.EF CartanMatrix.Relations.eF +#align cartan_matrix.relations.EF CartanMatrix.Relations.EF /-- The terms correpsonding to the `⁅H, E⁆`-relations. -/ -def hE : B × B → FreeLieAlgebra R (Generators B) := +def HE : B × B → FreeLieAlgebra R (Generators B) := uncurry fun i j => ⁅H i, E j⁆ - A i j • E j -#align cartan_matrix.relations.HE CartanMatrix.Relations.hE +#align cartan_matrix.relations.HE CartanMatrix.Relations.HE /-- The terms correpsonding to the `⁅H, F⁆`-relations. -/ -def hF : B × B → FreeLieAlgebra R (Generators B) := +def HF : B × B → FreeLieAlgebra R (Generators B) := uncurry fun i j => ⁅H i, F j⁆ + A i j • F j -#align cartan_matrix.relations.HF CartanMatrix.Relations.hF +#align cartan_matrix.relations.HF CartanMatrix.Relations.HF /-- The terms correpsonding to the `ad E`-relations. @@ -173,7 +173,7 @@ private theorem ad_F_of_eq_eq_zero (i : B) (h : A i i = 2) : adF R A ⟨i, i⟩ /-- The union of all the relations as a subset of the free Lie algebra. -/ def toSet : Set (FreeLieAlgebra R (Generators B)) := - (Set.range <| hH R) ∪ (Set.range <| eF R) ∪ (Set.range <| hE R A) ∪ (Set.range <| hF R A) ∪ + (Set.range <| HH R) ∪ (Set.range <| EF R) ∪ (Set.range <| HE R A) ∪ (Set.range <| HF R A) ∪ (Set.range <| adE R A) ∪ (Set.range <| adF R A) #align cartan_matrix.relations.to_set CartanMatrix.Relations.toSet @@ -200,6 +200,7 @@ deriving Inhabited, LieRing, namespace CartanMatrix +#print CartanMatrix.E₆ /- /-- The Cartan matrix of type e₆. See [bourbaki1968] plate V, page 277. The corresponding Dynkin diagram is: @@ -209,15 +210,17 @@ The corresponding Dynkin diagram is: o --- o --- o --- o --- o ``` -/ -def e₆ : Matrix (Fin 6) (Fin 6) ℤ := +def E₆ : Matrix (Fin 6) (Fin 6) ℤ := !![2, 0, -1, 0, 0, 0; 0, 2, 0, -1, 0, 0; -1, 0, 2, -1, 0, 0; 0, -1, -1, 2, -1, 0; 0, 0, 0, -1, 2, -1; 0, 0, 0, 0, -1, 2] -#align cartan_matrix.E₆ CartanMatrix.e₆ +#align cartan_matrix.E₆ CartanMatrix.E₆ +-/ +#print CartanMatrix.E₇ /- /-- The Cartan matrix of type e₇. See [bourbaki1968] plate VI, page 281. The corresponding Dynkin diagram is: @@ -227,7 +230,7 @@ The corresponding Dynkin diagram is: o --- o --- o --- o --- o --- o ``` -/ -def e₇ : Matrix (Fin 7) (Fin 7) ℤ := +def E₇ : Matrix (Fin 7) (Fin 7) ℤ := !![2, 0, -1, 0, 0, 0, 0; 0, 2, 0, -1, 0, 0, 0; -1, 0, 2, -1, 0, 0, 0; @@ -235,8 +238,10 @@ def e₇ : Matrix (Fin 7) (Fin 7) ℤ := 0, 0, 0, -1, 2, -1, 0; 0, 0, 0, 0, -1, 2, -1; 0, 0, 0, 0, 0, -1, 2] -#align cartan_matrix.E₇ CartanMatrix.e₇ +#align cartan_matrix.E₇ CartanMatrix.E₇ +-/ +#print CartanMatrix.E₈ /- /-- The Cartan matrix of type e₈. See [bourbaki1968] plate VII, page 285. The corresponding Dynkin diagram is: @@ -246,7 +251,7 @@ The corresponding Dynkin diagram is: o --- o --- o --- o --- o --- o --- o ``` -/ -def e₈ : Matrix (Fin 8) (Fin 8) ℤ := +def E₈ : Matrix (Fin 8) (Fin 8) ℤ := !![2, 0, -1, 0, 0, 0, 0, 0; 0, 2, 0, -1, 0, 0, 0, 0; -1, 0, 2, -1, 0, 0, 0, 0; @@ -255,8 +260,10 @@ def e₈ : Matrix (Fin 8) (Fin 8) ℤ := 0, 0, 0, 0, -1, 2, -1, 0; 0, 0, 0, 0, 0, -1, 2, -1; 0, 0, 0, 0, 0, 0, -1, 2] -#align cartan_matrix.E₈ CartanMatrix.e₈ +#align cartan_matrix.E₈ CartanMatrix.E₈ +-/ +#print CartanMatrix.F₄ /- /-- The Cartan matrix of type f₄. See [bourbaki1968] plate VIII, page 288. The corresponding Dynkin diagram is: @@ -264,10 +271,12 @@ The corresponding Dynkin diagram is: o --- o =>= o --- o ``` -/ -def f₄ : Matrix (Fin 4) (Fin 4) ℤ := +def F₄ : Matrix (Fin 4) (Fin 4) ℤ := !![2, -1, 0, 0; -1, 2, -2, 0; 0, -1, 2, -1; 0, 0, -1, 2] -#align cartan_matrix.F₄ CartanMatrix.f₄ +#align cartan_matrix.F₄ CartanMatrix.F₄ +-/ +#print CartanMatrix.G₂ /- /-- The Cartan matrix of type g₂. See [bourbaki1968] plate IX, page 290. The corresponding Dynkin diagram is: @@ -276,38 +285,49 @@ o ≡>≡ o ``` Actually we are using the transpose of Bourbaki's matrix. This is to make this matrix consistent with `cartan_matrix.F₄`, in the sense that all non-zero values below the diagonal are -1. -/ -def g₂ : Matrix (Fin 2) (Fin 2) ℤ := +def G₂ : Matrix (Fin 2) (Fin 2) ℤ := !![2, -3; -1, 2] -#align cartan_matrix.G₂ CartanMatrix.g₂ +#align cartan_matrix.G₂ CartanMatrix.G₂ +-/ end CartanMatrix namespace LieAlgebra +#print LieAlgebra.e₆ /- /-- The exceptional split Lie algebra of type e₆. -/ -abbrev E₆ := - CartanMatrix.e₆.ToLieAlgebra R -#align lie_algebra.e₆ LieAlgebra.E₆ +abbrev e₆ := + CartanMatrix.E₆.ToLieAlgebra R +#align lie_algebra.e₆ LieAlgebra.e₆ +-/ +#print LieAlgebra.e₇ /- /-- The exceptional split Lie algebra of type e₇. -/ -abbrev E₇ := - CartanMatrix.e₇.ToLieAlgebra R -#align lie_algebra.e₇ LieAlgebra.E₇ +abbrev e₇ := + CartanMatrix.E₇.ToLieAlgebra R +#align lie_algebra.e₇ LieAlgebra.e₇ +-/ +#print LieAlgebra.e₈ /- /-- The exceptional split Lie algebra of type e₈. -/ -abbrev E₈ := - CartanMatrix.e₈.ToLieAlgebra R -#align lie_algebra.e₈ LieAlgebra.E₈ +abbrev e₈ := + CartanMatrix.E₈.ToLieAlgebra R +#align lie_algebra.e₈ LieAlgebra.e₈ +-/ +#print LieAlgebra.f₄ /- /-- The exceptional split Lie algebra of type f₄. -/ -abbrev F₄ := - CartanMatrix.f₄.ToLieAlgebra R -#align lie_algebra.f₄ LieAlgebra.F₄ +abbrev f₄ := + CartanMatrix.F₄.ToLieAlgebra R +#align lie_algebra.f₄ LieAlgebra.f₄ +-/ +#print LieAlgebra.g₂ /- /-- The exceptional split Lie algebra of type g₂. -/ -abbrev G₂ := - CartanMatrix.g₂.ToLieAlgebra R -#align lie_algebra.g₂ LieAlgebra.G₂ +abbrev g₂ := + CartanMatrix.G₂.ToLieAlgebra R +#align lie_algebra.g₂ LieAlgebra.g₂ +-/ end LieAlgebra diff --git a/lake-manifest.json b/lake-manifest.json index 07ac6df96f..4b0b6232d6 100644 --- a/lake-manifest.json +++ b/lake-manifest.json @@ -10,15 +10,15 @@ {"git": {"url": "https://github.com/leanprover-community/lean3port.git", "subDir?": null, - "rev": "c27b70fc4256c52408e106112f288f6550e3977f", + "rev": "8d642a7f3193b6d2178c1c5c0004e3292a7ab377", "name": "lean3port", - "inputRev?": "c27b70fc4256c52408e106112f288f6550e3977f"}}, + "inputRev?": "8d642a7f3193b6d2178c1c5c0004e3292a7ab377"}}, {"git": {"url": "https://github.com/leanprover-community/mathlib4.git", "subDir?": null, - "rev": "bf799bb912c215766620a5a7133594b711412432", + "rev": "52608a673976368a55efd067ce4221588f8e6487", "name": "mathlib", - "inputRev?": "bf799bb912c215766620a5a7133594b711412432"}}, + "inputRev?": "52608a673976368a55efd067ce4221588f8e6487"}}, {"git": {"url": "https://github.com/gebner/quote4", "subDir?": null, diff --git a/lakefile.lean b/lakefile.lean index abfcd663e4..35094e1e82 100644 --- a/lakefile.lean +++ b/lakefile.lean @@ -4,7 +4,7 @@ open Lake DSL System -- Usually the `tag` will be of the form `nightly-2021-11-22`. -- If you would like to use an artifact from a PR build, -- it will be of the form `pr-branchname-sha`. -def tag : String := "nightly-2023-06-10-09" +def tag : String := "nightly-2023-06-10-11" def releaseRepo : String := "leanprover-community/mathport" def oleanTarName : String := "mathlib3-binport.tar.gz" @@ -38,7 +38,7 @@ target fetchOleans (_pkg : Package) : Unit := do untarReleaseArtifact releaseRepo tag oleanTarName libDir return .nil -require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"c27b70fc4256c52408e106112f288f6550e3977f" +require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"8d642a7f3193b6d2178c1c5c0004e3292a7ab377" @[default_target] lean_lib Mathbin where