Quotient Group is Unimodular Group
QuotientGroup.isUnimodularGroup
Plain-language statement
The quotient of a Hausdorff second countable unimodular group by a central normal closed subgroup is still unimodular.
Exact Lean statement
lemma _root_.QuotientGroup.isUnimodularGroup
{G : Type*} [Group G] [TopologicalSpace G] [IsUnimodularGroup G]
[T2Space G] [SecondCountableTopology G] (N : Subgroup G) [N.Normal]
(hN : N ≤ .center G) (hN' : IsClosed (X := G) N) : IsUnimodularGroup (G ⧸ N) where
modularCharacter_eq_oneFormal artifact
Lean source
lemma _root_.QuotientGroup.isUnimodularGroup {G : Type*} [Group G] [TopologicalSpace G] [IsUnimodularGroup G] [T2Space G] [SecondCountableTopology G] (N : Subgroup G) [N.Normal] (hN : N ≤ .center G) (hN' : IsClosed (X := G) N) : IsUnimodularGroup (G ⧸ N) where modularCharacter_eq_one := by ext g borelize G have H : MulDistribMulAction.toContinuousMulEquiv (ConjAct.toConjAct g) N = .refl _ := by ext x simp [-SetLike.coe_eq_coe, ConjAct.Subgroup.val_conj_smul, ConjAct.toConjAct_smul, ← ((hN x.prop).comm g).eq] have := modularCharacter_eq_modularCharacter_quotient_mul_mulEquivHaarChar N g simpa [IsUnimodularGroup.modularCharacter_eq_one, H] using this.symm- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/HaarMeasure/Quotient.lean:383-395
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Plain-language statement
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Source project: Fermat's Last Theorem
Person-level attribution pending.