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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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shuxuezhuyi
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@shuxuezhuyi shuxuezhuyi added awaiting-review t-algebra Algebra (groups, rings, fields etc) labels Oct 20, 2023
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Do you have plans to prove theorems about PSL using this definition?

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Do you have plans to prove theorems about PSL using this definition?

Yes, but I will not prove many theorems about PSL since I only know a little about algebra. I only need PSL(2, ℝ) to define the Fuchs group.

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Ok sounds good. Looking forward to seeing some Fuchsian groups.

maintainer merge

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🚀 Pull request has been placed on the maintainer queue by alexjbest.

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alexjbest commented Oct 21, 2023 •
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It would also be good to add some API like we have for SpecialLinearGroup
so things like

Coe (Matrix.ProjectiveSpecialLinearGroup n R) (Matrix n n R)

lemmas ext, ext_iff etc

Can you add that in this PR too actually?

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Actually thinking about it more, I'm not sure what lemmas even make sense, we don't have an actual coercion to matrices, so maybe this is fine like it is.

@eric-wieser eric-wieser self-assigned this Oct 21, 2023
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I suspect that it might be problematic to instance a coercion from PSL to SL, since there is no canonical embedding from PSL to SL.
Actually, I defined a function sl : PSL → SL:

noncomputable def sl (a : ProjectiveSpecialLinearGroup n R) :
    SpecialLinearGroup n R := Classical.choose a.exists_rep

And I used it to instance MulAction PSL(2, ℝ) ℍ. But I am also trying to see if I can avoid using it.

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eric-wieser commented Oct 21, 2023 •
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That sl looks like a bad idea to me

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digama0 commented Oct 21, 2023

Note: I have pushed an update to the lean toolchain because this PR was on a buggy version of the toolchain. WARNING: checking out old commits of this PR using v4.2.0-rc2 or v4.2.0-rc3 can cause lake clean to delete your mathlib folder! If you need to do so, make sure to delete lakefile.olean manually before running any lake commands.

This was referenced Oct 22, 2023
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@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Oct 31, 2023
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Dec 12, 2023
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This is a pretty bare definition, but unless someone has suggestions on what to add, I think we could merge it.

maintainer merge

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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

eric-wieser
eric-wieser reviewed Feb 16, 2024
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Mathlib/LinearAlgebra/Matrix/ProjectiveSpecialLinearGroup.lean
Comment on lines +28 to +30
/-- A projective special linear group is the quotient of a special linear group by its center.-/
abbrev ProjectiveSpecialLinearGroup : Type _ :=
SpecialLinearGroup n R ⧸ Subgroup.center (SpecialLinearGroup n R)
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Is X / Subgroup.Center X something worth naming in its own right?

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I think there is no standard name for this, so it would only confuse people.

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bors merge

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels Feb 23, 2024
mathlib-bors bot pushed a commit that referenced this pull request Feb 23, 2024
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feat(LinearAlgebra/Matrix): define projective special linear group (#…
fec1a64 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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mathlib-bors bot commented Feb 23, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(LinearAlgebra/Matrix): define projective special linear group [Merged by Bors] - feat(LinearAlgebra/Matrix): define projective special linear group Feb 23, 2024
@mathlib-bors mathlib-bors bot closed this Feb 23, 2024
@mathlib-bors mathlib-bors bot deleted the WenYang/PSL branch February 23, 2024 23:30
thorimur pushed a commit that referenced this pull request Feb 24, 2024
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feat(LinearAlgebra/Matrix): define projective special linear group (#…
45cef21 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
thorimur pushed a commit that referenced this pull request Feb 26, 2024
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feat(LinearAlgebra/Matrix): define projective special linear group (#…
c2095f4 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
riccardobrasca pushed a commit that referenced this pull request Mar 1, 2024
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@YaelDillies @riccardobrasca
feat(LinearAlgebra/Matrix): define projective special linear group (#…
e74bf3e 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
dagurtomas pushed a commit that referenced this pull request Mar 22, 2024
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feat(LinearAlgebra/Matrix): define projective special linear group (#…
26f0cf1 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
Louddy pushed a commit that referenced this pull request Apr 15, 2024
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feat(LinearAlgebra/Matrix): define projective special linear group (#…
deb0408 
…7791)




Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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