Geodesic
THE GROUP OF AUTOMORPHISMS OF THE FIRST WEYL ALGEBRA IN PRIME CHARACTERISTIC AND THE RESTRICTION MAP
Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 263-274

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Let K be a perfect field of characteristic p > 0; A1 := K〈x, ∂|∂x−x∂=1〉 be the first Weyl algebra; and Z:=K[X:=xp, Y:=∂p] be its centre. It is proved that (i) the restriction map res : AutK(A1)→ AutK(Z), σ ↦ σ|Z is a monomorphism with im(res) = Γ := {τ ∈ AutK(Z)|(τ)=1}, where (τ) is the Jacobian of τ, (Note that AutK(Z)=K* ⋉ Γ, and if K is not perfect then im(res) ≠ Γ.); (ii) the bijection res : AutK(A1) → Γ is a monomorphism of infinite dimensional algebraic groups which is not an isomorphism (even if K is algebraically closed); (iii) an explicit formula for res−1 is found via differential operators (Z) on Z and negative powers of the Fronenius map F. Proofs are based on the following (non-obvious) equality proved in the paper:
DOI : 10.1017/S0017089508004680
Mots-clés : 14J50, 16W20, 14L17, 14R10, 14R15, 14M20 
BAVULA, V. V. THE GROUP OF AUTOMORPHISMS OF THE FIRST WEYL ALGEBRA IN PRIME CHARACTERISTIC AND THE RESTRICTION MAP. Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 263-274. doi: 10.1017/S0017089508004680
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