Abstract
Let k be a field of positive characteristic p. We introduce the notion of a pseudo-derivation of a k-algebra A, and give a one-to-one correspondence between the set of all pseudo-derivations of A and the set of all p-unipotent automorphisms of A. We classify p-unipotent triangular automorphisms of a polynomial ring k[x, y, z] in three variables over k up to conjugation of automorphisms of k[x, y, z]. We prove that if a p-cyclic group ℤ/pℤ acts triangularly on the polynomial ring k[x, y, z], the modular invariant ring k[x, y, z]ℤ/pℤ is a hypersurface ring.
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TANIMOTO, R. PSEUDO-DERIVATIONS AND MODULAR INVARIANT THEORY. Transformation Groups 23, 271–297 (2018). https://doi.org/10.1007/s00031-017-9461-6
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DOI: https://doi.org/10.1007/s00031-017-9461-6