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New Stably Tame Automorphisms of Polynomial Algebras

✍ Scribed by Vesselin Drensky; Arno van den Essen; Dimitre Stefanov

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 93 KB
Volume: 226
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8224

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✦ Synopsis

Let K X Y = K x 1

x n y 1 y m be the polynomial algebra in m + n variables over a field K of characteristic 0. Let δ be a locally nilpotent derivation of K X Y such that δ y i = 0, i = 1 m, and let δ act as a K Y -affine transformation over the free K Y -module freely generated by x 1

x n . We prove that the automorphism exp wδ of K X Y is stably tame for every polynomial w from the kernel ker δ of δ. This result is applied to the automorphisms of the polynomial algebra in five variables introduced recently by Drensky and Gupta and arising from wild automorphisms of generic matrix algebras. We also give an algorithm for 1 Partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.

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