toAlgAutMulEquiv — Mathlib

English

There is a bijection between G and algebra homomorphisms fixing FixedPoints.subfield, when G is finite and acts faithfully on F.

Русский

Существует биекция между G и алгебраическими гомоморфизмами, фиксирующими FixedPoints.subfield, при условии конечности и FaithfulSMul.

LaTeX

$$$\\text{toAlgHom_bijective } G F : G \\to (\\operatorname{AlgHom}(\\operatorname{FixedPoints.subfield } G F, F))$ is bijective$$

Lean4

/-- Bijection between `G` and algebra automorphisms of `F` that fix the fixed points. -/
def toAlgAutMulEquiv [Finite G] [FaithfulSMul G F] : G ≃* (F ≃ₐ[FixedPoints.subfield G F] F) :=
  MulEquiv.ofBijective _ (toAlgAut_bijective G F)

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