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- W2972222070 abstract "We study the Zariski topology of the ind-groups of polynomial and free associative algebras $Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine space $Aut(K^n))$) and $Aut(K $ via $Ind$-schemes, toric varieties, approximations and singularities. We obtain some nice properties of $Aut(Aut(A))$, where $A$ is polynomial or free associative algebra over a field $K$. We prove that all $Ind$-scheme automorphisms of $Aut(K[x_1,...,x_n])$ are inner for $nge 3$, and all $Ind$-scheme automorphisms of $Aut(K )$ are semi-inner. We also establish that any effective action of torus $T^n$ on $Aut(K )$ is linearizable provided $K$ is infinity. That is, it is conjugated to a standard one. As an application, we prove that $Aut(K[x_1,...,x_n])$ cannot be embedded into $Aut(K )$ induced by the natural abelianization. In other words, the {it Automorphism Group Lifting Problem} has a negative solution. We explore the close connection between the above results and the Jacobian conjecture, and Kontsevich-Belov conjecture, and formulate the Jacobian conjecture for fields of any characteristic." @default.
- W2972222070 created "2019-09-12" @default.
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- W2972222070 date "2012-07-09" @default.
- W2972222070 modified "2023-09-27" @default.
- W2972222070 title "Lifting of the automorphism group of the polynomial algebras" @default.
- W2972222070 hasPublicationYear "2012" @default.
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