On automorphisms of affine superspaces
Bin Shu

TL;DR
This paper explores a super version of the Jacobian conjecture for affine superspaces, proving that certain homomorphisms satisfying a super Jacobian condition and preserving maximal ideals are automorphisms.
Contribution
It introduces a super Jacobian conjecture for affine superspaces and proves it under conditions involving preservation of maximal ideals, extending results to any characteristic.
Findings
Verified the super Jacobian conjecture when maximal ideal set is preserved.
Extended the conjecture's validity to fields of any characteristic.
Established conditions under which homomorphisms are automorphisms.
Abstract
In this note, we propose a super version of Jacobian conjecture on the automorphisms of affine superspaces over an algebraically closed field of characteristic , which predicts that for a homomorphism of the polynomial superalgebra over , if satisfies the super version of Jacobian condition (SJ for short), then gives rise to an automorphism of the affine superspace . We verify the conjecture if additionally, the set of maximal -homogeneous ideals of is assumed to be preserved under . The statement is actually proved in any characteristic, i.e. a homomorphism gives rise to an automorphism of if SJ is satisfied with and the set…
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems · Rings, Modules, and Algebras
