feat(Analysis/CStarAlgebra/Matrix): IsTopologicalGroup for specialUnitaryGroup

[anovickis]

Adds ContinuousInv and IsTopologicalGroup instances for Matrix.specialUnitaryGroup n 𝕜.

The unitary group Matrix.unitaryGroup n α already inherits these via the unitaryGroup ≡ unitary R abbrev + existing instances on unitary R (in Mathlib/Topology/Algebra/Star/Unitary.lean). However, specialUnitaryGroup is the sub-Submonoid unitaryGroup ⊓ MonoidHom.mker detMonoidHom — it does not auto-inherit those instances since it is not literally an alias of unitary R.

New declarations

• instance Matrix.specialUnitaryGroup.instContinuousInv — proven via Matrix.star_eq_inv + continuous_star
• instance Matrix.specialUnitaryGroup.instIsTopologicalGroup — combining ContinuousMul (from Submonoid structure) + ContinuousInv

Both placed inside the existing EntrywiseSupNorm section in Mathlib/Analysis/CStarAlgebra/Matrix.lean (the natural neighborhood for matrix-specific topological structure on (special) unitary groups).

Motivation

These instances enable using specialUnitaryGroup as a topological group in homogeneous-space constructions (e.g., SU(3) ⧸ T = F₂ flag manifolds). They complement #39146 (CompactSpace instances for the same groups) — together giving the standard 'compact topological group' typeclass set on specialUnitaryGroup.

Verification

```lean
example : ContinuousInv (Matrix.specialUnitaryGroup (Fin 3) ℂ) := inferInstance -- now works
example : IsTopologicalGroup (Matrix.specialUnitaryGroup (Fin 3) ℂ) := inferInstance -- now works
```

Both fail on master without this PR; both succeed after.

[github-actions]

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[github-actions]

PR summary 706bea155c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ Matrix.specialUnitaryGroup.instContinuousInv
+ Matrix.specialUnitaryGroup.instIsTopologicalGroup

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

---

No changes to strong technical debt.

No changes to weak technical debt.

[wwylele]

My comments in #39146 also applies here

• set_option backward.isDefEq.respectTransparency false is not necessary
• Matrix.Norms.Elementwise is not used in the statement/proof so it is not needed either. Given this, these should probably not placed in the EntrywiseSupNorm section

[j-loreaux]

I strongly suspect that you are using AI to write these PRs. That is against our AI policy for new contributors.

The entire reason we review PRs by new contributors is that it offers a teaching opportunity for them. If they use AI, the lessons are lost. I could implement all this myself faster than I could review it for you, so the only value comes if you are learning something.

Until you disclose your AI use I will not review any further PRs of yours.

[j-loreaux]

There's a much easier way via Topology.IsInducing.continuousInv. Also, we should have ContinuousStar for this type as well.