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Explain why the linear to AutF4 fails (for low dim reps)

This commit is contained in:
kalmar 2017-01-16 21:26:10 +01:00
parent f04cd75d73
commit 0ff0eefbd5

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@ -66,6 +66,16 @@ function generatingset_ofAutF(n::Int=N)
return S
end
#=
Note that the element
α(i,j,k) = ϱ(i,j)*ϱ(i,k)*inv(ϱ(i,j))*inv(ϱ(i,k)),
which surely belongs to ball of radius 4 in Aut(F₄) becomes trivial under the representation
Aut(F₄) GL₄()ℤ⁴ GL₅().
Moreover, due to work of Potapchik and Rapinchuk [1] every real representation of Aut(Fₙ) into GLₘ() (for m 2n-2) factors through GLₙ()ℤⁿ, so will have the same problem.
We need a different approach!
=#
const ID = eye(N+1)
const S₁ = generatingset_ofAutF(N)