On automorphisms of tame polynomial automorphism Ind-Schemes in positive characteristic

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In this paper we study certain combinatorial attributes of Ind -schemes of polynomial automorphisms in positive characteristic. In particular, we prove that over an algebraically closed field K of positive characteristic ≠ 2 every automorphism of the group of origin-preserving automorphisms of the polynomial algebra K [ x 1 , … , x n ] ( n ≥ 3 ), which fixes every diagonal matrix, preserves, up to composition with a linear inner automorphism, every tame automorphism.