Frontiers of Mathematics in China >

2007 , Vol. 2 >Issue 1: 13 - 46

DOI: https://doi.org/10.1007/s11464-007-0002-9

Coordinates and automorphisms of polynomial and free associative algebras of rank three

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  • 1.Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria; 2.Department of Mathematics, University of Hong Kong, Hong Kong, China;

Published date: 05 Mar 2007

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Abstract

We study z-automorphisms of the polynomial algebra K[x, y, z] and the free associative algebra K[x, y, z]over a field K, i.e., automorphisms that fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For K[x, y, z] we include also results about the structure of the z-tame automorphisms and algorithms that recognize z-tame automorphisms and z-tame coordinates.

Cite this article

Vesselin Drensky, Jie-Tai Yu . Coordinates and automorphisms of polynomial and free associative algebras of rank three[J]. Frontiers of Mathematics in China, 2007 , 2(1) : 13 -46 . DOI: 10.1007/s11464-007-0002-9

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