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Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.det_mapGL

∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {S : Type u_1}
  [inst_3 : CommRing S] [inst_4 : Algebra R S] (g : Matrix.SpecialLinearGroup n R),
  Matrix.GeneralLinearGroup.det ((Matrix.SpecialLinearGroup.mapGL S) g) = 1
Defined in
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
Cited by
1 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqFintypeCommRingCommRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UpperHalfPlane.coe_specialLinearGroup_apply · cited by 10UpperHalfPlane.coe_specia…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraFintype · cited by 7736FintypeAlgebra.algebraMap · cited by 4706Algebra.algebraMapMatrix · cited by 4303MatrixMonoidHom · cited by 3629MonoidHomUnits · cited by 2804UnitsMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupMatrix.SpecialLinearGroup · cited by 348Matrix.SpecialLinearGroupMatrix.SpecialLinearGroup.mapGL · cited by 98SpecialLinearGroup.mapGLMatrix.SpecialLinearGroup.map · cited by 77SpecialLinearGroup.mapMatrix.GeneralLinearGroup.det · cited by 58GeneralLinearGroup.detMatrix.SpecialLinearGroup.coeToGL_det · cited by 10SpecialLinearGroup.coeToG…SpecialLinearGroup.det_mapGLCITED BYCITES

Cites14

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Cited by1

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