Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.lineStab_smul

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι]
  (g : Matrix.SpecialLinearGroup ι F) (L : Submodule F (ι → F)),
  Matrix.SpecialLinearGroup.lineStab (g • L) = MulAut.conj g • Matrix.SpecialLinearGroup.lineStab L

Equivariance of lineStab under conjugation by elements of SL.

Defined in: Mathlib.LinearAlgebra.Projectivization.PSL.Stabilizer
Cited by: 0 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field DecidableEq Fintype

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DFunLike.coestatement and proof · cited by 62,936
Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
MonoidHomstatement · cited by 3,629
Subgroupstatement · cited by 3,593
Matrix.SpecialLinearGroupstatement and proof · cited by 348
SemigroupAction.mul_smulproof · cited by 291
smul_addproof · cited by 263
add_sub_cancel_rightproof · cited by 187
MulAutstatement · cited by 158
smul_subproof · cited by 142

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