Skip to content

Commit

Permalink
bump to nightly-2023-06-10-11
Browse files Browse the repository at this point in the history
  • Loading branch information
leanprover-community-bot committed Jun 10, 2023
1 parent 33e3da9 commit 4f055b6
Show file tree
Hide file tree
Showing 3 changed files with 60 additions and 40 deletions.
88 changes: 54 additions & 34 deletions Mathbin/Algebra/Lie/CartanMatrix.lean
Expand Up @@ -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.
Expand Down Expand Up @@ -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
Expand All @@ -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:
Expand All @@ -209,15 +210,17 @@ The corresponding Dynkin diagram is:
o --- o --- o --- o --- o
```
-/
def e : 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:
Expand All @@ -227,16 +230,18 @@ The corresponding Dynkin diagram is:
o --- o --- o --- o --- o --- o
```
-/
def e : 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;
0, -1, -1, 2, -1, 0, 0;
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:
Expand All @@ -246,7 +251,7 @@ The corresponding Dynkin diagram is:
o --- o --- o --- o --- o --- o --- o
```
-/
def e : 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;
Expand All @@ -255,19 +260,23 @@ 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:
```
o --- o =>= o --- o
```
-/
def f : 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:
Expand All @@ -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 g : 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

8 changes: 4 additions & 4 deletions lake-manifest.json
Expand Up @@ -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,
Expand Down
4 changes: 2 additions & 2 deletions lakefile.lean
Expand Up @@ -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"

Expand Down Expand Up @@ -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
Expand Down

0 comments on commit 4f055b6

Please sign in to comment.