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[Merged by Bors] - feat(LinearAlgebra/Matrix): define projective special linear group #7791

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[Merged by Bors] - feat(LinearAlgebra/Matrix): define projective special linear group #7791

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feat(LinearAlgebra/Matrix): define projective special linear group
shuxuezhuyi Oct 20, 2023
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docs
shuxuezhuyi Oct 20, 2023
99598c4
use abbrev instead of def
shuxuezhuyi Oct 21, 2023
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notation docstring
shuxuezhuyi Oct 21, 2023
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chore: bump lean toolchain
digama0 Oct 21, 2023
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Merge branch 'master' into WenYang/PSL
YaelDillies Dec 12, 2023
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use abbrev instead of def
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shuxuezhuyi committed Oct 21, 2023
commit 99598c4410853d0755597bb21bd271c8b7c2113f
11 changes: 1 addition & 10 deletions Mathlib/LinearAlgebra/Matrix/ProjectiveSpecialLinearGroup.lean
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Expand Up @@ -20,17 +20,8 @@ open scoped MatrixGroups
variable (n : Type u) [DecidableEq n] [Fintype n] (R : Type v) [CommRing R]

/-- A projective special linear group is the quotient of a special linear group by its center.-/
def ProjectiveSpecialLinearGroup :=
abbrev ProjectiveSpecialLinearGroup :=
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SpecialLinearGroup n R ⧸ Subgroup.center (SpecialLinearGroup n R)

/-- `PSL(n, R)` is the projective special linear group `SL(n, R)/Z(SL(n, R))`.-/
scoped[MatrixGroups] notation "PSL(" n ", " R ")" => Matrix.ProjectiveSpecialLinearGroup (Fin n) R

namespace ProjectiveSpecialLinearGroup

instance : Group (ProjectiveSpecialLinearGroup n R) :=
QuotientGroup.Quotient.group <| Subgroup.center (SpecialLinearGroup n R)

instance : Inhabited (ProjectiveSpecialLinearGroup n R) := ⟨1⟩

end ProjectiveSpecialLinearGroup